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"---\n",
"title: \"Convergence of Finite Differences\"\n",
"subtitle: \"Lecture 13\"\n",
"date: 2026-03-23\n",
"abstract-title: Overview\n",
"format:\n",
" html:\n",
" other-links:\n",
" - text: This notebook\n",
" href: L13.ipynb\n",
"---"
]
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"::: {.callout-note}\n",
"\n",
"I encourage you to play around with the juptyer notebook for this lecture - you can copy the code with the ```this notebook``` button on the side of this page.\n",
"\n",
":::\n",
"\n",
"::: {.callout-warning}\n",
"\n",
"These notes are mainly a record of what we discussed and are not a substitute for attending the lectures and reading books! If anything is unclear/wrong, let me know and I will update the notes.\n",
"\n",
":::\n",
"\n",
"::: {.callout-tip}\n",
"\n",
"This chapter is mostly based on \n",
"\n",
"* @Burden Chapter 11, \n",
"* @FNC Chapter 10\n",
"\n",
":::"
]
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"#| echo: false\n",
"\n",
"using Plots, LaTeXStrings, LinearAlgebra\n",
"\n",
"# IF YOU ARE READING THIS, THANK YOU\n",
"# FOR DOWNLOADING THE LECTURE NOTES.\n",
"# THE FIRST PERSON TO LET ME KNOW,\n",
"# WINS SOME CHOCOLATES OF YOUR CHOICE"
]
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"## Recap\n",
"\n",
"We are considering boundary value problems of the following form: Suppose we have a differential operator $\\mathcal L$, a \"nice\" domain $\\Omega \\subset \\mathbb R^d$, and *data* $f$. Seek $u : \\Omega \\to \\mathbb R$ such that \n",
"\n",
"\\begin{align}\n",
" \\mathcal L[u] &= f &&\\text{in } \\Omega \\nonumber\\\\\n",
" u &= 0 &&\\text{on } \\partial \\Omega .\n",
" \\tag{BVP}\n",
"\\end{align}\n",
"\n",
"This is a problem with *homogeneous Dirichlet boundary conditions* (the values of the solution are prescribed on the boundary (Dirichlet) and are zero (homogeneous)).\n",
"\n",
"::: {#exm-BVPs}\n",
"# Linear Advection-Diffusion-Reaction Equations\n",
"\n",
"Consider\n",
"\n",
"\\begin{align}\n",
" \\mathcal L[u] := -\\Delta u + p \\cdot \\nabla u + q u\n",
"\\end{align}\n",
"\n",
"In the context of semiconductor physics, $u(x)$ represents the concentration of charge carriers at a position $x \\in \\Omega$. Each of these terms relates to the physics in question: \n",
"\n",
"* $-\\Delta$ : diffusion; electrons move from areas of high concentration to low, \n",
"* $p \\cdot \\nabla u$ : advection (drift); the solution is driven with velocity $p$ (due to e.g. an external electric field), \n",
"* $q u$ : reaction; electrons and electron holes are being created or destroyed.\n",
"\n",
"The same equation also models e.g pollutant transport in a river, drug delivery in a blood vessel, asset price in finance, heat transfer in fluids, ...... \n",
"\n",
":::\n",
"\n",
"Last time, we solved this equation on $[0,1]$ numerically using finite differences: we defined the mesh $\\{x_j\\}_{j=0}^n$ with $x_j = \\frac{j}{n}$ and *mesh size* $h= \\frac{1}{n}$ and approximated $u_j \\approx u(x_j)$. \n",
"\n",
"::: {#exr-}\n",
"\n",
"Write down the resulting linear system of equations that resulted from using finite differences - check with the person next to you.\n",
"\n",
":::\n",
"\n",
"By approximating the continuous problem with finite differences, we obtain a discrete problem: find $\\bm U \\in \\mathbb R^{n+1}$ (with index starting at $0$ or equivalently $U: \\Omega_h \\to \\mathbb R$ where $\\Omega_h := \\{x_j\\}_{j=0}^n \\to \\mathbb R$ with $U_j := U(x_j)$) such that \n",
"\n",
"\\begin{align}\n",
" \\begin{split}\n",
" &\\mathcal L_h [\\bm U] = \\bm f \\\\\n",
" &U_0 = U_n = 0 \n",
" \\end{split}\\tag{$\\text{BVP}_h$}\n",
"\\end{align}\n",
"\n",
"where $\\mathcal L_h$ depends on the choice of finite difference scheme.\n",
"\n",
"::: {#exm-}\n",
"\n",
"In the example we saw on Monday, we have \n",
"\n",
"\\begin{align}\n",
" \\mathcal L_h &= -L + p D^0 + qI \\nonumber\\\\\n",
" %\n",
" &= -\\frac{1}{h^2} \n",
" \\begin{pmatrix}\n",
" -2 & 1 & & & \\\\\n",
" 1 & -2 & 1 & & \\\\\n",
" & 1 & -2 & \\ddots \\\\\n",
" & & \\ddots & \\ddots & 1\\\\\n",
" & & & 1 & -2 \n",
" \\end{pmatrix}\n",
" %\n",
" + \\frac{p}{2h} \n",
" \\begin{pmatrix}\n",
" 0 & 1 & & & \\\\\n",
" -1 & 0 & 1 & & \\\\\n",
" & -1 & 0 & \\ddots \\\\\n",
" & & \\ddots & \\ddots & 1\\\\\n",
" & & & -1 & 0 \n",
" \\end{pmatrix}\n",
" % \n",
" + q I, \\nonumber\n",
"\\end{align}\n",
"\n",
"a $(n-1)\\times(n-1)$ matrix (acting on the interior points of the grid).\n",
"\n",
":::\n",
"\n",
"Recall, we say that a numerical approximation is *consistent* if the error converges when you substitute in the exact solution of the problem. In this particular setting, we have:\n",
"\n",
"::: {#def-consistent}\n",
"# Consistency\n",
"\n",
"Suppose that $u : \\Omega \\to \\mathbb R$ is the exact solution to $\\text{(BVP)}$ and let $\\bm u = \\{ u(x_j) \\}_{j=0}^n$ be the exact solution evaluated on the mesh. We say the numerical approximation $(\\text{BVP}_h)$ is *consistent* if $\\| \\mathcal L_h[\\bm u] - \\bm f\\|_{\\infty} \\to 0$ as $h \\to 0$ where $f_j = f(x_j)$. \n",
"\n",
"We say the numerical approximation is *order-$p$ accurate* (or has *order of accuracy $p$*) if $\\| \\mathcal L_h[\\bm u] - \\bm f\\|_{\\infty} = O(h^p)$ as $h \\to 0$. \n",
"\n",
":::\n",
"\n",
"::: {#def-convergent}\n",
"# Convergence\n",
"\n",
"Suppose that $u : \\Omega \\to \\mathbb R$ is the exact solution to $\\text{(BVP)}$ and let $\\bm u$ be the exact solution restricted to the mesh. Let $\\bm U_h$ be the numerical solution to $(\\text{BVP}_h)$. We say the numerical scheme is *convergent* if $\\| \\bm U_h - \\bm u \\|_{\\infty} \\to 0$ as $h \\to 0$.\n",
"\n",
"We say the numerical approximation is *convergent of order-$p$* if $\\| \\bm U_h - \\bm u \\|_{\\infty} = O(h^p)$ as $h \\to 0$. \n",
"\n",
":::\n",
"\n",
"::: {#def-stable}\n",
"# Stability\n",
"\n",
"We say that $(\\text{BVP}_h)$ is stable if there exists $C>0$ such that \n",
"\n",
"\\begin{align}\n",
" \\| \\bm U_h - \\bm W_h \\|_{\\infty} \\leq C \\| \\mathcal L_h[\\bm U_h] - \\mathcal L_h[\\bm W_h] \\|_{\\infty}\n",
"\\end{align}\n",
"\n",
"for all $\\bm U_h, \\bm W_h$.\n",
"\n",
":::\n",
"\n",
"Again, stability means that if we have data $\\bm f$ and $\\bm f + \\bm \\delta$ (for example, we have data and the corresponding floating-point representation of the data) and corresponding numerical solutions $\\bm U_h$ and $\\bm W_h$ (resp.), then stability means $\\bm W_h$ is close to $\\bm U_h$. \n",
"\n",
"::: {.callout-note}\n",
"\n",
"These notions all depend on the choice of norm. We choose $\\| \\cdot \\|_{\\infty}$ for simplicity.\n",
"\n",
":::\n",
"\n",
"\n",
"We have the theorem that you should be expecting: \n",
"\n",
"::: {#thm-fundamental}\n",
"\n",
"Suppose that $\\text{(BVP)}$ and $(\\text{BVP}_h)$ have unique solutions $u$ and $\\bm U_h$. Then, if $(\\text{BVP}_h)$ is consistent (with order $p$) and stable then the method is convergent (with order at least $p$).\n",
"\n",
":::\n",
"\n",
"::: {.box}\n",
"\n",
"***Proof.*** \n",
"\n",
"Let $\\bm u$ be the exact solution to the continuous problem restricted to the mesh and suppose that $(\\text{BVP}_h)$ is order $p$ accurate. Then, by stability, we have \n",
"\n",
"\\begin{align}\n",
" \\| \\bm U_h - \\bm u \\|_\\infty &\\leq C \\| \\mathcal L_h[\\bm U_h] - \\mathcal L_h[\\bm u] \\|_\\infty \\nonumber\\\\\n",
" %\n",
" &= C \\| \\bm f - \\mathcal L_h[\\bm u] \\|_\\infty \\nonumber\\\\\n",
" %\n",
" &= O(h^p)\n",
"\\end{align}\n",
"\n",
"as $h\\to0$. (The final equality is the consistency estimate).\n",
"\n",
":::\n",
"\n",
"## Convergence of finite differences for ADR \n",
"\n",
"Here, we return to the linear Advection-Diffusion-Reaction equation in 1d: \n",
"\n",
"\\begin{align}\n",
" &\\mathcal L[u] := -u'' + p u' + q u = f \\nonumber\\\\\n",
" &u(0) = u(1) = 0, \\nonumber\n",
"\\end{align}\n",
"\n",
"and the numerical scheme\n",
"\n",
"\\begin{align}\n",
" &\\mathcal L_h[\\bm U] := (-L + p D^0 + q I) \\bm U = \\bm f \\nonumber\\\\\n",
" &U_0 = U_n = 0.\n",
"\\end{align}\n",
"\n",
"In the following, we show that the method is consistent and (under some assumptions on the parameters $p,q$) stable. We can then use the theorem to conclude that the method is convergent. \n",
"\n",
"::: {#exr-}\n",
"# Consistency\n",
"\n",
"What is the order of accuracy of the approximate scheme? \n",
"\n",
":::\n",
"\n",
"We now move on to stability. We will use the following notion: \n",
"\n",
"::: {#def-SDD}\n",
"# Strictly Diagonally Dominant (SDD)\n",
"\n",
"A matrix $A$ is *SDD* if \n",
"\n",
"\\begin{align}\n",
" |A_{ii}| > \\sum_{j \\not= i} |A_{ij}|\n",
"\\end{align}\n",
"\n",
"for all $i$.\n",
"\n",
":::\n",
"\n",
"For what parameters $p,q$ is the matrix \n",
"\n",
"\\begin{align}\n",
"\\mathcal L_h = \\frac{1}{h^2} \n",
" \\begin{pmatrix}\n",
" 2 + h^2q & -1+\\frac{p}{2} h & & & \\\\\n",
" -1-\\frac{p}{2}h & 2 + h^2q & -1+\\frac{p}{2}h & & \\\\\n",
" & -1-\\frac{p}{2}h & 2 + h^2q & \\ddots \\\\\n",
" & & \\ddots & \\ddots & -1+\\frac{p}{2}h\\\\\n",
" & & & -1-\\frac{p}{2}h & 2 + h^2q \n",
" \\end{pmatrix}\n",
" %\n",
"\\end{align}\n",
"\n",
"SDD for all sufficiently small $h$?\n",
"\n",
"::: {#lem-SDD}\n",
"\n",
"Suppose $A$ is an SDD matrix. Then, $A$ is invertible and there exists $C$ such that \n",
"\n",
"\\begin{align}\n",
" \\|x\\|_\\infty \\leq C \\| Ax\\|_{\\infty} .\n",
"\\end{align}\n",
"\n",
":::\n",
"\n",
"::: {.box}\n",
"\n",
"**Proof.**\n",
"\n",
"Take $i$ such that $|x_i| = \\|x\\|_\\infty$ and notice that, if $A x = b$, then $b_i = A_{ii} x_i + \\sum_{j\\not= i} A_{ij} x_j$ and so \n",
"\n",
"\\begin{align}\n",
" |A_{ii}||x_i| &\\leq |b_i| + \\sum_{j\\not= i} |A_{ij}| |x_j| \\nonumber\\\\\n",
" %\n",
" &\\leq |b_i| + \\sum_{j\\not= i} |A_{ij}| |x_i|. \n",
"\\end{align}\n",
"\n",
"Since $|x_i| = \\|x\\|_\\infty$, we have \n",
"\n",
"\\begin{align}\n",
" \\Bigg( |A_{ii}| - \\sum_{j\\not= i} |A_{ij}|\\Bigg) \\|x\\|_{\\infty} &\\leq |b_i| \\nonumber\n",
"\\end{align}\n",
"\n",
"and, since $A$ is SDD, we have \n",
"\n",
"\\begin{align}\n",
" \\|x\\|_\\infty &\\leq \\Bigg( |A_{ii}| - \\sum_{j\\not= i} |A_{ij}|\\Bigg)^{-1} |b_i|\n",
" %\n",
" \\nonumber\\\\\n",
" %\n",
" &\\leq C \\|b\\|_\\infty = C \\|Ax\\|_\\infty \n",
"\\end{align}\n",
"\n",
"where $C = \\max_i \\big( |A_{ii}| - \\sum_{j\\not= i} |A_{ij}|\\big)^{-1}$. \n",
"\n",
":::"
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"::: {#exr-}\n",
"\n",
"Show that, for $p \\in\\mathbb R$ and $q > 0$, the approximation scheme $(\\text{BVP}_h)$ is stable for all $h < \\frac{2}{|p|}$.\n",
"\n",
":::\n",
"\n",
"We apply our numerical scheme to this problem and plot the error between the exact solution and the approximate scheme. (Hopefully) we will see that our method converges with rate $O(h^2)$ for the choice of $p,q$ mentioned above. We also plot the error when using a forward difference of order of accuracy $1$ instead of the central difference for approximating $q u'$ (what do you expect to see in the error plots?):"
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",
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
""
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function adr_1d(n, p, q, f; order=2)\n",
" h = 1/n \n",
" x = h:h:(1-h) \n",
" \n",
" # Finite Difference Coefficients\n",
" # -u'' ≈ (-u_{i-1} + 2u_i - u_{i+1}) / h^2\n",
" # use central difference (order of accuracy 2)\n",
" # pu' ≈ p * (u_{i+1} - u_{i-1}) / (2h) \n",
" # or forward difference (order of accuracy 1)\n",
" # pu' ≈ p * (u_{i+1} - u_{i}) / h \n",
" if (order == 1)\n",
" # use the forward difference D^+ = (u_j+1-u_j)/h\n",
" d = (2/h^2 + q - p/h) * ones(n-1)\n",
" d₋ = (-1/h^2 ) * ones(n-2)\n",
" d₊ = (-1/h^2 + p/h) * ones(n-2)\n",
" else\n",
" # use a central difference D^0 = (u_j+1 - u_j-1)/2h\n",
" d = (2/h^2 + q) * ones(n-1)\n",
" d₋ = (-1/h^2 - p/(2h)) * ones(n-2)\n",
" d₊ = (-1/h^2 + p/(2h)) * ones(n-2)\n",
" end\n",
"\n",
" A = Tridiagonal(d₋, d, d₊)\n",
" b = f.(x)\n",
" u = A \\ b\n",
"\n",
" # Dirichlet boundary conditions\n",
" u = [0.0, u..., 0.0]\n",
" x = [0.0, x..., 1.0]\n",
"\n",
" return x, u\n",
"end\n",
"\n",
"# u'' = diffusion\n",
"# p = advection\n",
"# q = reaction\n",
"# f = source \n",
"\n",
"f(x) = 1.0 \n",
"\n",
"# Advection\n",
"p, q = 50., 0.\n",
"x, u = adr_1d(100, p, q, f)\n",
"P1 = plot(x, u, title=L\"Diffusion: $-u′′ + %$p u′ + %$q u = 1$\", \n",
" xlabel=L\"Position $x$\", ylabel=L\"Concentration $u$\",\n",
" label=L\"u(x)\", lw=2, m=1)\n",
"u_e(x) = (x - (exp(50*x)-1)/(exp(50)-1))/50\n",
"plot!(P1, u_e, linestyle=:dot, label=\"exact solution\")\n",
"display(P1)\n",
"\n",
"hh = [2.0^(-n) for n=10:-1:2]\n",
"errs1 = zeros(length(hh))\n",
"errs2 = zeros(length(hh))\n",
"for (i,h) ∈ enumerate(hh)\n",
" x, u1 = adr_1d(round(Int, 1/h), p, q, f; order=1)\n",
" x, u2 = adr_1d(round(Int, 1/h), p, q, f; order=2)\n",
" errs1[i] = norm( u1 - u_e.(x) , Inf ) \n",
" errs2[i] = norm( u2 - u_e.(x) , Inf ) \n",
"end\n",
"P2 = plot( [hh hh], [errs1 errs2];\n",
" color=[:red :blue], label=[\"using forward difference\" \"using central difference\"],\n",
" xaxis=:log, yaxis=:log, title=L\"errors in $||\\cdot||_\\infty$\", m=3 ) \n",
"plot!( hh, hh/4; \n",
" xlabel=L\"h\", linestyle=:dash, label=L\"O(h)\", color=:red)\n",
"plot!( hh, hh.^2; \n",
" linestyle=:dash, label=L\"O(h^2)\", color=:blue)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "7222e981",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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""
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},
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},
{
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Reaction (decay)\n",
"p, q = 0., 100.\n",
"x, u = adr_1d(100, p, q, f)\n",
"P3 = plot(x, u, title=L\"Reaction: $-u′′ + %$p u′ + %$q u = 1$\", \n",
" xlabel=L\"Position $x$\", ylabel=L\"Concentration $u$\",\n",
" label=L\"u(x)\", lw=2, m=1)\n",
"u_e(x) = ( 1 - (sinh(10x)+sinh(10(1-x)))/(sinh(10)) )/100\n",
"plot!(P3, u_e, linestyle=:dot, label=\"exact solution\")\n",
"display(P3)\n",
"\n",
"hh = [2.0^(-n) for n=10:-1:2]\n",
"errs = zeros(length(hh))\n",
"for (i,h) ∈ enumerate(hh)\n",
" x, u = adr_1d(round(Int, 1/h), p, q, f)\n",
" errs[i] = norm( u - u_e.(x) , Inf ) \n",
"end\n",
"P2 = plot( hh, errs;\n",
" primary=false, \n",
" xaxis=:log, yaxis=:log, title=L\"errors in $||\\cdot||_\\infty$\", m=3, color=:red ) \n",
"plot!( hh, hh.^2/100; \n",
" xlabel=L\"h\", linestyle=:dash, label=L\"O(h^2)\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "cf44c6b3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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},
{
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Advection + Reaction\n",
"p, q = 100., 100.\n",
"x, u = adr_1d(100, p, q, f)\n",
"P4 = plot(x, u, title=L\"$-u′′ + %$p u′ + %$q u = 1$\", \n",
" xlabel=L\"Position $x$\", ylabel=L\"Concentration $u$\",\n",
" label=L\"u(x)\", lw=2, m=1)\n",
"r1 = 100.99\n",
"r2 = -.99\n",
"u_e(x) = .01*( 1 - exp(r1*x) * (1-exp(r2))/(exp(r1)-exp(r2)) - exp(r2*x) * (exp(r1)-1)/(exp(r1)-exp(r2)) )\n",
"plot!(P4, u_e, linestyle=:dot, label=\"exact solution\")\n",
"display(P4)\n",
"\n",
"hh = [2.0^(-n) for n=10:-1:2]\n",
"errs = zeros(length(hh))\n",
"for (i,h) ∈ enumerate(hh)\n",
" x, u = adr_1d(round(Int, 1/h), p, q, f)\n",
" errs[i] = norm( u - u_e.(x) , Inf ) \n",
"end\n",
"P2 = plot( hh, errs;\n",
" primary=false, \n",
" xaxis=:log, yaxis=:log, title=L\"errors in $||\\cdot||_\\infty$\", m=3, color=:red ) \n",
"plot!( hh, hh.^2; \n",
" xlabel=L\"h\", linestyle=:dash, label=L\"O(h^2)\")"
]
},
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"source": [
"::: {#exr-}\n",
"\n",
"***1.*** What is the stability constant $C$ that you get by following the proof of the lemma ($A$ SDD implies stability $\\|x\\|_\\infty \\leq C \\|Ax\\|_\\infty$) when applied to $\\mathcal L_h$?\n",
"\n",
"***2.*** Is this constant what you observe numerically? If $C$ is larger, how does this change the error curve?\n",
"\n",
":::\n",
"\n",
"Next: \n",
"\n",
"* ($L^\\infty$) Stability of $-L \\bm U = \\bm F$ (here, $L$ is not SDD!)\n",
"* More generally, stability of finite difference schemes which give rise to irreducible diagonally dominant (IDD) matrices,\n",
"* $L^2$ stability"
]
},
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"source": [
":::{.callout-tip}\n",
"# TO-DO\n",
"\n",
"* Take a quick look at the suggestions for [Presentations/Posters/Papers](/Presentations.html), \n",
"* (Sign-up to office hours if you would like)\n",
"\n",
"Chapter 1 reading:\n",
"\n",
"* @Burden sections 5.1 - 5.6, \n",
"* @FNC [zero stability](https://fncbook.com/zerostability/) \n",
"\n",
"Chapter 2 reading:\n",
"\n",
"* Recap matrices: sections 7.1 - 7.2 of @Burden \n",
"* Jacobi & Gauss-Seidel: section 7.3 @Burden \n",
"* CG: section 7.6 @Burden\n",
"\n",
"Chapter 3 reading: \n",
"\n",
"* Sections 11.1 - 11.2 of @Burden: shooting methods\n",
"\n",
":::"
]
}
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