From a0c2b196457039515d60743d70717432bac02e64 Mon Sep 17 00:00:00 2001 From: FPaquin Date: Wed, 11 Nov 2015 10:39:08 -0800 Subject: [PATCH] First commit --- hom4_p4.eps | 2542 +++++++++++++++++++++++++++++++++++ test_accuracy_cos_neumann.m | 56 + 2 files changed, 2598 insertions(+) create mode 100644 hom4_p4.eps create mode 100644 test_accuracy_cos_neumann.m diff --git a/hom4_p4.eps b/hom4_p4.eps new file mode 100644 index 0000000..36760a9 --- /dev/null +++ b/hom4_p4.eps @@ -0,0 +1,2542 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: (MATLAB, The Mathworks, Inc. Version 8.5.0.197613 \(R2015a\). Operating System: Windows 8) +%%Title: ./hom4_p4.eps +%%CreationDate: 2015-11-10T11:43:48 +%%Pages: (atend) +%%BoundingBox: (atend) +%%LanguageLevel: 3 +%%EndComments +%%BeginProlog +%%BeginResource: procset (Apache XML Graphics Std ProcSet) 1.2 0 +%%Version: 1.2 0 +%%Copyright: (Copyright 2001-2003,2010 The Apache Software Foundation. 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+214.264 444.149 L +213.5 446.5 L +214.264 448.851 L +216.264 450.304 L +218.736 450.304 L +220.736 448.851 L +221.5 446.5 L +S +GR +GS +[0.75 0 0 0.75 0 0] CT +0 0 1 RC +2 setlinecap +10.0 ML +N +176.5 489.5 M +175.736 487.149 L +173.736 485.696 L +171.264 485.696 L +169.264 487.149 L +168.5 489.5 L +169.264 491.851 L +171.264 493.304 L +173.736 493.304 L +175.736 491.851 L +176.5 489.5 L +S +GR +GS +[0.75 0 0 0.75 298.1253 30.18751] CT +/Helvetica-Bold 15 F +GS +[1 0 0 1 0 0] CT +-145.5 -4 moveto +1 -1 scale +(Convergence study, u\(x\)=cos\(x\) on [0,pi]) t +GR +GR +%%Trailer +%%BoundingBox: 34 11 528 416 +%%Pages: 1 +%%EOF diff --git a/test_accuracy_cos_neumann.m b/test_accuracy_cos_neumann.m new file mode 100644 index 0000000..bb25145 --- /dev/null +++ b/test_accuracy_cos_neumann.m @@ -0,0 +1,56 @@ +function output = test_accuracy_cos_neumann(plots, verbose) +%test_accuracy_sin Verify accuracy of the "1 -2 1" method with Neumann +%boundary condition. Test function is u(x) = cos(x), u''(x) = -cos(x). +% Log-log plot is produced. Order accuracy is calculated with polyfit. + +% Frederic Paquin-Lefebvre + +if nargin == 0 + plots = false; + verbose = false; +elseif nargin == 1 + verbose = false; +end + +a=0; +b=pi; +Err=[]; +h=[]; + +for i=2:10 + N=2^i; + x=linspace(a,b,N)'; + dx=x(2)-x(1); + [Ix,D1xx,D1xc,D1xb,D1xf] = diff_matrices1d(N, dx, 'n'); + u=cos(x); + uxx_exact=-cos(x); + D2u=D1xx*u; + Err(i-1)=norm(D2u-uxx_exact); + h(i-1)=dx; +end + +coeff=polyfit(log(h),log(Err),1); +disp('Order of accuracy');disp(coeff(1)); + +if plots + h1=figure(1); + loglog(h,Err,'-ob') + title('Convergence study, u(x)=cos(x) on [0,pi]') + xlabel('step h') + ylabel('Error') +end + +if verbose + if abs(coeff(1)-2) < 1e-1 + % test passed + output=true; + disp('Test passed') + else + % test failed + output=false; + disp('Test failed') + end +end + +print(h1,'hom4_p4','-depsc') +end \ No newline at end of file