{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Error Control and Variable Step Sizes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**References:**\n",
"\n",
"- Section 6.5 *Variable Step-Size Methods* in {cite}`Sauer`.\n",
"- Section 5.5 *Error Control and the Runge-Kutta-Fehlberg Method* in {cite}`Burden-Faires`.\n",
"- Section 7.3 in {cite}`Chenney-Kincaid`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Basic ODE Initial Value Problem\n",
"\n",
"We consider again the initial value problem\n",
"\n",
"$$ \\frac{d u}{d t} = f(t, u) \\quad a \\leq t \\leq b, \\quad u(a) = u_0 $$\n",
"\n",
"We now allow the possibility that $u$ and $f$ are vector-valued as in the section\n",
"{doc}`ODE-IVP-4-system-higher-order-equations`,\n",
"but omitting the tilde notation $\\tilde u$, $\\tilde f$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Error Control by Varying the Time Step Size $h_i$\n",
"\n",
"Recall the variable step-size version of Euler's method:\n",
"\n",
"```{prf:algorithm}\n",
":label: euler-variable-h\n",
"\n",
"Input: $f$, $a$, $b$, $n$ \n",
"\n",
"$t_0 = a$\n",
" \n",
"$U_0 = u_0$\n",
" \n",
"$h = (b-a)/n$\n",
" \n",
"for i in $[0, n)$:\n",
" \n",
"$\\qquad$ Choose step size $h_i$ somehow!\n",
" \n",
"$\\qquad$ $t_{i+1} = t_i + h_i$\n",
" \n",
"$\\qquad$ $U_{i+1} = U_i + h_i f(t_i, U_i)$\n",
" \n",
"end\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now consider how to choose each step size, by estimating the error in each step,\n",
"and aiming to have error per unit time below some limit like $\\epsilon/(b-a)$, so that the global error is no more than about $\\epsilon$.\n",
"\n",
"As usual, the theoretical error bounds like $O(h_i^2)$ for a single step of Euler's method are not enough for quantitative tasks like choosing $h_i$,\n",
"but they do motivate more practical estimates."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A crude error estimate for Euler's Method: Richardson Extrapolation\n",
"\n",
"Starting at a point (t, u(t)), we can estimate the error in Euler's method approximato at a slightly later time $t_i + h$ by using two approximations of $U(t + h)$:\n",
"- The value given by a step of Euler's method with step size $h$: call this $U^{h}$\n",
"- The value given by taking two steps of Euler's method each with step size $h/2$: call this $U_2^{h/2}$,\n",
"because it involves 2 steps of size $h/2$.\n",
"\n",
"The first order accuracy of Euler's method gives $e_h = u(t+h) - U^{h} \\approx 2(u(t+h) - U_2^{h/2})$,\n",
"so that\n",
"\n",
"$$e_h \\approx \\frac{U_2^{h/2} - U^{h}}{2}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step size choice\n",
"\n",
"What do we do with this error information?\n",
"\n",
"The first obvious ideas are:\n",
"- Accept this step if $e_h$ is small enough, taking $h_i = h$, $t_{i+1} = t_i + h_i$, and $U_{i+1} = U^h$, but\n",
"- reject it and try again with a smaller $h$ value otherwise; maybe halving $h$; but there are more sophisticated options too."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See [Exercise 1](exercise-1)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Error tolerance \n",
"\n",
"One simple criterion for accuracy is that the estimated error in this step be no more than some overall upper limit on the error in each time step, $T$.\n",
"That is, accept the step size $h$ if\n",
"\n",
"$$|e_h| \\leq T$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### A crude approach to reducing the step size when needed\n",
"\n",
"If this error tolerance is not met, we must choose a new step size $h'$, and we can predict roughly its error behavior using the known order natue of the error in Euler's method: scaling dowen to $h' = s h$, the error in a single step scales with $h^2$ (in general it scales with $h^{p+1}$ for a method of order $p$), and so to reduce the error by the needed factor $\\displaystyle \\frac{e_h}{T}$ one needs approximately\n",
"\n",
"$$ s^2 = \\frac{T}{|e_h|} $$\n",
"\n",
"and so using $e_h \\approx \\tilde{e}_h = |U^{h/2} - U^{h}|$ suggests using\n",
"\n",
"$$ s = \\left( \\frac{T}{|U^{h/2} - U^{h}|} \\right)^{1/2} $$\n",
"\n",
"However this new step size might have error that is still slightly too large, leading to a second failure.\n",
"Another is that one might get into an infinite loop of step size reduction.\n",
"\n",
"So refinements of this choice must be considered."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Increasing the step size when desirable\n",
"\n",
"If we simply follow the above aproach, the step size, once reduced, will never be increased.\n",
"This could lead to great inefficiency, through using an unecessarily small step size just because at an earlier part of the time domain, accuracy required very small steps.\n",
"\n",
"Thus, after a successful time step, one might consider increasing $h$ for the next step.\n",
"This could be done using exactly the above formula, but again there are risks, so again refinement of this choice must be considered.\n",
"\n",
"One problem is that if the step size gets too large, the error estimate can become unreliable; another is that one might need some minimum \"temporal resolution\", for nice graphs and such.\n",
"\n",
"Both suggest imposing an upper limit on the step size $h$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Another strategy for getting error estimates: two (related) Runge-Kutta methods\n",
"\n",
"The recurring strategy of estimating errors by the difference of two different approximations — one expected to be far better than the other — can be used in a nice way here.\n",
"I will first illustrate with the simplest version, using Euler's Mathod and the Explicit Trapezoid Method.\n",
"\n",
"Recall that the increment in Euler's Method from time $t$ to time $t+h$ is\n",
"\n",
"$$K_1 = h f(t, U)$$\n",
"\n",
"whereas for the Explict Trapezoid Method it is $(K_1 + K_2)/2$, as given by\n",
"\n",
"$$\\begin{split}\n",
"K_1 &= h f(t, U)\n",
"\\\\\n",
"K_2 &= h f(t+h, U + K_1)\n",
"\\end{split}$$\n",
"\n",
"Thus we can use the difference, $|K_1 - (K_1 + K_2)/2| = |(K_1 - K_2)/2|$ as an error estimate.\n",
"In fact to be cautious, one often drops the factor of $1/2$, so using approximation $\\tilde{e}_h = |K_1 - K_2|$.\n",
"\n",
"One has to be careful: this estimates the error in Euler's Method, and one has to use it that way:\n",
"using the less accurate value $K_1$ as the update.\n",
"\n",
"A basic algorithm for the time step starting with $t_i, U_i$ is"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{prf:algorithm}\n",
":label: choose-step-size-1\n",
"\n",
"$K_1 \\leftarrow h f(t_i, U_i)$\n",
" \n",
"$K_2 \\leftarrow h f(t_i + h, U_i + K_1)$\n",
" \n",
"$e_h \\leftarrow |K_1 - K_2|$\n",
" \n",
"$s \\leftarrow \\sqrt{T/e_h}$\n",
" \n",
"if $e_h < T$\n",
" \n",
"$\\quad U_{i+1} = U_i + K_1$\n",
" \n",
"$\\quad t_{i+1} = t_i + h$\n",
" \n",
"$\\quad$ Increase $h$ for the *next* time step:\n",
" \n",
"$\\quad h \\leftarrow s h$\n",
" \n",
"else: $\\quad$ (not good enough: reduce $h$ and try again)\n",
" \n",
"$\\quad h \\leftarrow s h$\n",
" \n",
"$\\quad$ Start again from $K_1 = \\dots$\n",
" \n",
"end\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, in practice one needs:\n",
"\n",
"- An upper limit $h_{max}$ on the step size $h$, partly because error estimates become unreliable if $h$ gets too large,\n",
"and also becuase subsequent use of the results (like graphs) might need sufficiently \"fine\" data.\n",
"\n",
"- A lower limit $h_{max}$ on $h$, to avoid infinite loops and such.\n",
"\n",
"- Since we are using only an approximation $\\tilde{e}_h$ of $e_h$, and out of general caution,\n",
"it is typical to include a \"safety factor\" of about $0.8$ or $0.9$, when computing the *next* time step: reducing the step size scale factor to $S = 0.9 \\sqrt{T/e_h}$.\n",
"\n",
"Incorporating these refinements:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{prf:algorithm}\n",
":label: choose-step-size-2\n",
"\n",
"$K_1 = h f(t_i, U_i)$\n",
" \n",
"$K_2 = h f(t_i+h, U_i + K_1)$\n",
" \n",
"$e_{h} = |K_1 - K_2|$\n",
" \n",
"$s = 0.9\\sqrt{T/e_h}$\n",
" \n",
"if $e_h < T$\n",
" \n",
"$\\quad U_{i+1} = U_i + K_1$\n",
" \n",
"$\\quad t_{i+1} = t_i + h$\n",
" \n",
"$\\quad$ Increase $h$ for the *next* time step:\n",
" \n",
"$\\quad h \\leftarrow \\min(0.9 s h, h_{max})$\n",
" \n",
"else: $\\quad$ (not good enough; reduce $h$ and try again)\n",
" \n",
"$\\quad h \\leftarrow \\max(0.9 s h, h_{min})$\n",
" \n",
"$\\quad$ Start again from $K_1 = \\dots$\n",
" \n",
"end\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See [Exercise 2](exercise-2)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## The explicit trapezoid method with error control\n",
"\n",
"In practice, one usually needs at least second order accuracy, and one approach to that is using computing a \"candidates\" for the next time step with a second order accurate Runge-Kutta method and also a third order accurate one, the latter used only to get an error estimate for the former.\n",
"\n",
"Perhaps the simplest of these is based on adding error estimation to the Explicit Trapezoid Rule.\n",
"Omitting the step size adjustment for now, the main ingredients are:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{prf:algorithm}\n",
":label: trapezoid-step-size\n",
"\n",
"$K_1 = h f(t, U)$\n",
" \n",
"$K_2 = h f(t + h, U + K_1)$\n",
" \n",
"(So far, as for the explicit trapezoid method)\n",
"\n",
"$K_3 = h f(t + h/2, U + (K_1 + K_2)/4)$\n",
" \n",
"(a midpoint approximation, using the above)\n",
"\n",
"$\\delta_2 = (K_1 + K_2)/2$\n",
" \n",
"(The order 2 increment as for the explicit trapezoid method)\n",
"\n",
"$\\delta_3 = (K_1 + 4 K_3 + K_2)/6$\n",
" \n",
"(An order 3 increment — note the resemblance to Simpson's Rule for integration.\n",
"This is only used to get the final error estimate below)\n",
"\n",
"$e_h = |\\delta_2 - \\delta_3 |, \\, = |K_1 -2 K_3 + K_2|/3$\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, if this step is accepted, one uses the explicit trapezoid rule step: $U_{i+1} = U_i + \\delta_2$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step size adjustment\n",
"\n",
"The scale factor $s$ for step size adjustment must be modified for a method order $p$ (with $p=2$ now):\n",
"- Changing step size by a factor $s$ will change the error $e_h$ in a single time step by a factor of about $s^{p+1}$.\n",
"\n",
"- Thus, we want a new step with this rescaled error of about $s^{p+1} e_h$ roughly matching the tolerance $T$.\n",
"Equating would give $s^{p+1} e_h = T$, so $s = (T/e_h))^{1/(p+1)}$,\n",
"but as noted above, since we are using only an approximation $\\tilde{e}_h$ of $e_h$\n",
"it is typical to include a \"safety factor\" of about $0.9$, so something like\n",
"\n",
"$$s = 0.9 \\left( \\frac{T}{|\\tilde{e}_h|} \\right)^{1/(p+1)}$$\n",
"\n",
"Thus for this second order accurate method, we then get\n",
"\n",
"$$s = 0.9 \\left( \\frac{3 T}{|K_1 -2 K_3 + K_2|} \\right)^{1/3}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**A variant: relative error control**\n",
"\n",
"One final refinement: it is more common in software to impose a *relative error* bound: aiming for $|e_h/u(t)| \\leq T$,\n",
"or $|e_h| \\leq T|u(t)|$.\n",
"Approximating $u(t)$ by $U_i$, this changes the step size rescaling guideline to\n",
"\n",
"$$s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/(p+1)}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See [Exercise 3](exercise-3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fourth order accurate methods with error control: Runge-Kutta-Felberg and some newer refinements\n",
"\n",
"The details involve some messy coefficients; see the references above for those.\n",
"\n",
"The basic idea is to devise a fifth order accurate Runge-Kutta method such that we can also get a fourth order accurate method from the same colection of *stages* $K_i$ values.\n",
"One catch is that any such fifth order method requires six stages (not five as you might have guessed).\n",
"\n",
"The first such method, still widely used, is the\n",
"[Runge-Kutta-Felberg Method](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%E2%80%93Fehlberg_method)\n",
"published by Erwin Fehlberg in 1970:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{prf:algorithm} RUnge-Kutta-Fehlberg\n",
":label: rkf\n",
"\n",
"$K_1 = h f(t, U)$\n",
" \n",
"$K_2 = f(t + \\frac{1}{4}h, U + K_1/4)$\n",
" \n",
"$K_3 = f(t + \\frac{3}{8} h, U + \\frac{3}{32} K_1 + \\frac{9}{32} K_2)$\n",
" \n",
"$K_4 = f(t + \\frac{12}{13} h, U + \\frac{1932}{2197} K_1 - \\frac{7200}{2197} K_2 + \\frac{7296}{2197} K_3)$\n",
" \n",
"$K_5 = f(t + h, U + \\frac{439}{216} K_1 - 8 K_2 + \\frac{3680}{2565} K_3 - \\frac{845}{4104} K_4)$\n",
" \n",
"$K_6 = f(t + \\frac{1}{2}h, U - \\frac{8}{27} K_1 + 2 K_2 - \\frac{3544}{513} K_3 + \\frac{1859}{4104} K_4 - \\frac{11}{40} K_5)$\n",
" \n",
"$\\delta_4 = \\frac{25}{216} K_1 + \\frac{1408}{2565} K_3 + \\frac{2197}{4104} K_4 - \\frac{1}{5} K_5$\n",
" \n",
"(The order 4 increment that will actually be used)\n",
"\n",
"$\\delta_5 = \\frac{16}{135} K_1 + \\frac{6656}{12825} K_3 + \\frac{28561}{56430} K_4 - \\frac{9}{50} K_5 + \\frac{2}{55} K_6$\n",
" \n",
"(The order 5 increment, used only to get the following error estimate)\n",
"\n",
"$\\tilde{e}_h = \\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5 + \\frac{2}{55} K_6$\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This method is typically used with the relative error control mentioned above, and since the order is $p=4$,\n",
"the recommended step-size rescaling factor is\n",
"\n",
"$$s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/5},\n",
"= 0.9 \\left| \\frac{T U_i}{\\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5 + \\frac{2}{55} K_6} \\right|^{1/5},\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ODE solvers in Julia package `DifferentialEquations`\n",
"\n",
"Newer software often uses variants such as the\n",
"method of [Dormand–Prince method](https://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method) published in 1980\n",
"or that of Tsitouras published in 2011.\n",
"\n",
"These (and many others) are available in the Julia package `DifferentialEquations` as `DP5` and `Tsit45` respectively."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example using package `DifferentialEquations`\n",
"\n",
"To be added."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Exercises"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### Exercise 1\n",
"\n",
"Write a formula for $U_h$ and $e_h$ if one starts from the point $(t_i, U_i)$, so that $(t_i + h, U^h)$ is the proposed value for the next point $(t_{i+1}, U_{i+1})$ in the approximate solution — but only if $e_h$ is small enough!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### Exercise 2\n",
"\n",
"Implement {prf:ref}`choose-step-size-2`, and test on the two familiar examples\n",
"\n",
"$$\n",
"\\begin{split}\n",
"du/dt &= Ku\n",
"\\\\\n",
"&\\text{and}\n",
"\\\\\n",
"du/dt &= K(\\cos(t) - u) - \\sin(t)\n",
"\\end{split}\n",
"$$\n",
"\n",
"($K=1$ is enough.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### Exercise 3\n",
"\n",
"Implement [the explicit trapezoid method with error control](#etmec)\n",
"as sketched out in {prf:ref}`trapezoid-step-size`,\n",
"and test on the two familiar examples\n",
"\n",
"$$\n",
"\\begin{split}\n",
"du/dt &= K u\n",
"\\\\\n",
"&\\text{and}\n",
"\\\\\n",
"du/dt &= K(\\cos(t) - u) - \\sin(t)\n",
"\\end{split}\n",
"$$\n",
"\n",
"($K = 1$ is enough.)"
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"#### Partial Solution to Exercise 2"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using PyPlot\n",
"using LinearAlgebra: norm"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import Base: round\n",
"round(x,n) = round(x,sigdigits=n);"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"function eulermethod_errorcontrol(f, a, b, u_0; errortolerance=1e-3, h_min=1e-6, h_max=0.1, steps_max=1000, demomode=false)\n",
" steps = 0\n",
" t_i = a\n",
" U_i = u_0\n",
" t = [t_i]\n",
" U = [U_i]\n",
" h = h_max # Start optimistically!\n",
" while t_i < b && steps < steps_max\n",
" K_1 = h*f(t_i, U_i)\n",
" K_2 = h*f(t_i + h/2, U_i + K_1/2)\n",
" errorestimate = abs(K_1 - K_2)\n",
" s = 0.9 * sqrt(errortolerance/errorestimate)\n",
" if errorestimate <= errortolerance # Success!\n",
" t_i += h\n",
" U_i += K_1\n",
" append!(t, t_i)\n",
" append!(U, U_i)\n",
" # Adjust step size up, but not too big\n",
" h = min(s*h, h_max)\n",
" else # Innacurate; reduce step size and try again\n",
" h = max(s*h, h_min)\n",
" if demomode\n",
" println(\"t_i=$t_i: Decreasing step size to $(round(h,4)) and trying again.\")\n",
" end\n",
" end\n",
" # A refinement not mentioned above; the next step should not overshoot t=b:\n",
" if t_i + h > b\n",
" h = b - t_i\n",
" end\n",
" steps += 1\n",
" end\n",
" return (t, U)\n",
" # Note: if the step count ran out, this does not reach t=b, but at least it is correct as far as it goes\n",
"end;"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"f(t, u) = K*u;"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"a = 1.0\n",
"b = 3.0\n",
"u_0 = 2.0\n",
"K = 1.0\n",
"u(t) = u_0*exp(K*(t-a));"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t_i=1.0: Decreasing step size to 0.09 and trying again.\n",
"\n",
"With error tolerance 0.01, this took 36 time steps, of average length 0.05556\n",
"The maximum absolute error is 0.8311\n",
"The maximum absolute error per time step is 0.02309\n",
"The time taken to solve was 0.1013 seconds\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject )"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject )"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"errortolerance = 1e-2\n",
"time_start = time()\n",
"(t, U) = eulermethod_errorcontrol(f, a, b, u_0; errortolerance=errortolerance, demomode=true)\n",
"time_end = time()\n",
"time_elapsed = time_end - time_start\n",
"\n",
"steps = length(U) - 1\n",
"h_ave = (b-a)/steps\n",
"U_exact = u.(t)\n",
"U_error = U_exact - U\n",
"U_max = norm(U_error, Inf)\n",
"println()\n",
"println(\"With error tolerance $errortolerance, this took $steps time steps, of average length $(round(h_ave,4))\")\n",
"println(\"The maximum absolute error is $(round(U_max,4))\")\n",
"println(\"The maximum absolute error per time step is $(round(U_max/steps,4))\")\n",
"println(\"The time taken to solve was $(round(time_elapsed,4)) seconds\")\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Solution to du/dt=$(K)u, u($a)=$u_0\")\n",
"plot(t, U, \".:\")\n",
"grid(true)\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Error in the above\")\n",
"plot(t, U_error, \".:\")\n",
"grid(true);"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t_i=1.0: Decreasing step size to 0.02846 and trying again.\n",
"\n",
"With error tolerance 0.001, this took 119 time steps, of average length 0.01681\n",
"The maximum absolute error is 0.2648\n",
"The maximum absolute error per time step is 0.002225\n",
"The time taken to solve was 0.000737 seconds\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject )"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject )"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"errortolerance = 1e-3\n",
"time_start = time()\n",
"(t, U) = eulermethod_errorcontrol(f, a, b, u_0; errortolerance=errortolerance, demomode=true)\n",
"time_end = time()\n",
"time_elapsed = time_end - time_start\n",
"\n",
"steps = length(U) - 1\n",
"h_ave = (b-a)/steps\n",
"U_exact = u.(t)\n",
"U_error = U_exact - U\n",
"U_max = norm(U_error, Inf)\n",
"println()\n",
"println(\"With error tolerance $errortolerance, this took $steps time steps, of average length $(round(h_ave,4))\")\n",
"println(\"The maximum absolute error is $(round(U_max,4))\")\n",
"println(\"The maximum absolute error per time step is $(round(U_max/steps,4))\")\n",
"println(\"The time taken to solve was $(round(time_elapsed,4)) seconds\")\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Solution to du/dt=$(K)u, u($a)=$u_0\")\n",
"plot(t, U, \".:\")\n",
"grid(true)\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Error in the above\")\n",
"plot(t, U_error, \".:\")\n",
"grid(true);"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t_i=1.0: Decreasing step size to 0.009 and trying again.\n",
"\n",
"With error tolerance 0.0001, this took 380 time steps, of average length 0.005263\n",
"The maximum absolute error is 0.08398\n",
"The maximum absolute error per time step is 0.000221\n",
"The time taken to solve was 0.00068 seconds\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject )"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject )"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"errortolerance = 1e-4\n",
"time_start = time()\n",
"(t, U) = eulermethod_errorcontrol(f, a, b, u_0; errortolerance=errortolerance, demomode=true)\n",
"time_end = time()\n",
"time_elapsed = time_end - time_start\n",
"\n",
"steps = length(U) - 1\n",
"h_ave = (b-a)/steps\n",
"U_exact = u.(t)\n",
"U_error = U_exact - U\n",
"U_max = norm(U_error, Inf)\n",
"println()\n",
"println(\"With error tolerance $errortolerance, this took $steps time steps, of average length $(round(h_ave,4))\")\n",
"println(\"The maximum absolute error is $(round(U_max,4))\")\n",
"println(\"The maximum absolute error per time step is $(round(U_max/steps,4))\")\n",
"println(\"The time taken to solve was $(round(time_elapsed,4)) seconds\")\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Solution to du/dt=$(K)u, u($a)=$u_0\")\n",
"plot(t, U)\n",
"grid(true)\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Error in the above\")\n",
"plot(t, U_error)\n",
"grid(true);"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.8.1",
"language": "julia",
"name": "julia-1.8"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}