Home > K25104 > ODEs > backward_euler_script_1.m

backward_euler_script_1

PURPOSE ^

Usage example for backward_euler

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

 Usage example for backward_euler
 related to question 6.1

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % Usage example for backward_euler
0002 % related to question 6.1
0003 
0004 f = @(t,y) -y/(1+t);
0005 t0 = 0;
0006 y0 = 1;
0007 h = 0.1;
0008 T = 1;
0009 analytic = @(t) 1./(1+t);
0010 [ y,t,err ] = backward_euler( f,t0,y0,h,T,analytic );
0011 figure;
0012 plot(t,y,'o');           
0013 xlabel('t');
0014 ylabel('y(t)');
0015 hold on;
0016 ezplot(analytic, [0 1]);
0017 legend('numerical','analytic');
0018 f = @(t,y) 2*y/(1+t);
0019 analytic = @(t) (1+t).^2;
0020 [ y,t,err ] = backward_euler( f,t0,y0,h,T,analytic );
0021 figure;
0022 plot(t,y,'o');           
0023 xlabel('t');
0024 ylabel('y(t)');
0025 hold on;
0026 ezplot(analytic, [0 1]);
0027 legend('numerical','analytic');
0028 
0029

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