{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Error Control and Variable Step Sizes\n",
"\n",
"**Version of 2022-10-09**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**References:**\n",
"\n",
"- Section 6.5 *Variable Step-Size Methods* in [Sauer](../frontmatter/references.html#Sauer)\n",
"- Section 5.5 *Error Control and the Runge-Kutta-Fehlberg Method* in [Burden&Faires](../frontmatter/references.html#Burden-Faires)\n",
"- Section 7.3 of [Chenney&Kincaid](../frontmatter/references.html#Chenney-Kincaid)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Basic ODE Initial Value Problem\n",
"\n",
"We consider again the initial value problem\n",
"\n",
"$$\n",
"\\frac{d u}{d t} = f(t, u) \\quad a \\leq t \\leq b, \\quad u(a) = u_0\n",
"$$\n",
"\n",
"We now allow the possibility that $u$ and $f$ are vector-valued as in the section on\n",
"[Systems of ODEs and Higher Order ODEs](ODE-IVP-4-system-higher-order-equations-julia.ipynb),\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",
"Input: $f$, $a$, $b$, $n$ \n",
"\n",
"$t_0 = a$ \n",
"$U_0 = u_0$ \n",
"$h = (b-a)/n$ \n",
"\n",
"for i in $[0, n)$:\n",
" \n",
"\n",
"$\\qquad$ Choose step size $h_i$ somehow!\n",
" \n",
"\n",
"$\\qquad$ $t_{i+1} = t_i + h_i$\n",
" \n",
"\n",
"$\\qquad$ $U_{i+1} = U_i + h_i f(t_i, U_i)$\n",
" \n",
"\n",
"end for\n",
"\n",
"We now consider how to choose each step size, by estimating the error in each step, 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 $h_i$, 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": [
"---\n",
"\n",
"### Exercise A\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!\n",
"\n",
"---"
]
},
{
"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",
"$$\n",
"s^2 = \\frac{T}{|e_h|}\n",
"$$\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 simplset 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": [
"$K_1 \\leftarrow h f(t_i, U_i)$\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 if"
]
},
{
"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": [
"$K_1 = h f(t_i, U_i)$\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 if"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### Exercise B\n",
"\n",
"Implement the above, 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.)\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Partial Solution to Exercise B"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using PyPlot\n",
"using LinearAlgebra: norm"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"about (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# TO DO? Add this to module NumericalMethods\n",
"about(x) = round(x,sigdigits=3)"
]
},
{
"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 $(about(h)) 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.\n",
"b = 3.\n",
"u_0 = 2.\n",
"K = 1.5\n",
"\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 0.06 and trying again.\n",
"\n",
"With error tolerance 0.01, this took 74 time steps, of average length 0.027\n",
"The maximum absolute error is 2.77\n",
"The maximum absolute error per time step is 0.0374\n",
"The time taken to solve was 0.133 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 $(about(h_ave))\")\n",
"println(\"The maximum absolute error is $(about(U_max))\")\n",
"println(\"The maximum absolute error per time step is $(about(U_max/steps))\")\n",
"println(\"The time taken to solve was $(about(time_elapsed)) seconds\")\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Solution to du/dt=$(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 0.019 and trying again.\n",
"\n",
"With error tolerance 0.001, this took 241 time steps, of average length 0.0083\n",
"The maximum absolute error is 0.884\n",
"The maximum absolute error per time step is 0.00367\n",
"The time taken to solve was 0.000652 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 $(about(h_ave))\")\n",
"println(\"The maximum absolute error is $(about(U_max))\")\n",
"println(\"The maximum absolute error per time step is $(about(U_max/steps))\")\n",
"println(\"The time taken to solve was $(about(time_elapsed)) seconds\")\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Solution to du/dt=$(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": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t_i=1.0: Decreasing step size to 0.006 and trying again.\n",
"\n",
"With error tolerance 0.0001, this took 770 time steps, of average length 0.0026\n",
"The maximum absolute error is 0.28\n",
"The maximum absolute error per time step is 0.000364\n",
"The time taken to solve was 0.00205 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 $(about(h_ave))\")\n",
"println(\"The maximum absolute error is $(about(U_max))\")\n",
"println(\"The maximum absolute error per time step is $(about(U_max/steps))\")\n",
"println(\"The time taken to solve was $(about(time_elapsed)) seconds\")\n",
"\n",
"figure(figsize=[10,4])\n",
"title(\"Solution to du/dt=$(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": "markdown",
"metadata": {},
"source": [
"## 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 teh 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": [
"$K_1 = h f(t, U)$\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:)\n",
"\n",
"$e_h = |\\delta_2 - \\delta_3 |, \\, = |K_1 -2 K_3 + K_2|/3$"
]
},
{
"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": [
"---\n",
"\n",
"### Exercise C\n",
"\n",
"Implement this\n",
"[error control version of the explicit trapezoid method](#ETMEC),\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.)\n",
"\n",
"---"
]
},
{
"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": [
"$K_1 = h f(t, U)$\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",
"$\\tilde{e}_h = \\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5 + \\frac{2}{55} K_6$"
]
},
{
"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",
"$$\n",
"s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/5},\n",
"= 0.9 \\left| \\frac{T U_i}{\\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5 + \\frac{2}{55} K_6} \\right|^{1/5},\n",
"$$\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` — to be added"
]
}
],
"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
}