Home > K25104 > ODEs > explicit_RK_script_2.m

explicit_RK_script_2

PURPOSE ^

Usage example for explicit_RK

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

 Usage example for explicit_RK
 employing the original Runge-Kutta method

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % Usage example for explicit_RK
0002 % employing the original Runge-Kutta method
0003 
0004 f = @(t,y) -10^2*(y - t^(-1)) - t^(-2);
0005 t0 = 1;
0006 y0 = 1;
0007 h = 0.029;
0008 % no increase in error if h =0.028
0009 T = 2;
0010 b = [1/6; 1/3; 1/3; 1/6];
0011 c = [0; 1/2; 1/2; 1];
0012 A = [0 0 0 0;
0013     1/2 0 0 0;
0014     0 1/2 0 0;
0015     0 0 1 0];
0016 analytic = @(t) t.^(-1);
0017 [ y,t,err ] = explicit_RK( f,t0,y0,h,T,b,c,A,analytic );
0018 figure;
0019 plot(t,y,'o');           
0020 xlabel('t');
0021 ylabel('y(t)');
0022 hold on;
0023 ezplot(analytic, [1 2]);
0024 legend('numerical','analytic');

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