solution_hw12 - y(1,i+1)=y(1,i)+(k11+2*k21+2*k31+k41)*h/6;

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function [f1 f2]=fun(x,y,z) f1=-2*y+5*exp(-x); f2=-y*z^2/2; function [y]=RungeKutta(fun,xint,yint,xfinal,h) x=xint:h:xfinal; y(1,1)=yint(1); y(2,1)=yint(2); n=length(x) for i=1:n-1 [k11 k12]=feval(fun,x(i),y(1,i),y(2,i)); [k21 k22]=feval(fun,x(i)+h/2,y(1,i)+k11*h/2,y(2,i)+k12*h/2); [k31 k32]=feval(fun,x(i)+h/2,y(1,i)+k21*h/2,y(2,i)+k22*h/2); [k41 k42]=feval(fun,x(i)+h/2,y(1,i)+k31*h,y(2,i)+k32*h);
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Unformatted text preview: y(1,i+1)=y(1,i)+(k11+2*k21+2*k31+k41)*h/6; y(2,i+1)=y(2,i)+(k12+2*k22+2*k32+k42)*h/6; end figure(1) plot(x,y(1,:), 'o-' ,x,y(2,:), '*-' ); title( 'RungeKutta method' ); xlabel( 'x' ); ylabel( 'y' ); grid on ; x0=0; y0=[2 4]'; h=0.2; xf=1; y=RungeKutta( 'fun' ,x0,y0,xf,h) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 2.5 3 3.5 4 RungeKutta method x y...
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This note was uploaded on 04/21/2010 for the course PGE 310 taught by Professor Klaus during the Spring '06 term at University of Texas.

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solution_hw12 - y(1,i+1)=y(1,i)+(k11+2*k21+2*k31+k41)*h/6;

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