hw17_derek_rampal

hw17_derek_rampal - Derek Rampal HW 17 17 10/20 5.7 232...

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HW 17 17 10/20 5.7 232 1(a), 2(a) Use the Runge-Kutta method of order 4. Compute the actual values, the absolute errors and the number of significant digits. code: % % Derek Rampal % 17 10/20 5.7 232 1(a), 2(a) % clear; % 1a a1 = 0; b1 = 1; h1 =.2; ival1 = [1;1]; ffun = inline( '[3*y(1)+2*y(2)-(2*t^2+1)*exp(2*t);4*y(1)+y(2)+(t^2+2*t- 4)*exp(2*t)]' , 't' , 'y' ); fact = inline( '[1/3,-1/3,1;1/3,2/3,t^2]*exp([5;-1;2]*t)' , 't' ); [t1,onea] = rk4(ffun,a1,b1,h1,ival1); [m,n] = size(t1); [m1,n1]=size(onea); for i = 1:m oneaact(:,i) = fact(t1(i,1)); for j = 1:m1 [sd(j,i),abserr(j,i),relerr(j,i)] = sigdig(oneaact(j,i),onea(j,i)); end ; end ; [t1';onea] oneaact abserr relerr sd % 2a % y''-2*y'+y=t*exp(t)-t % u1(t)=y(t) % u1'(t)=u2(t)=y'(t) % u2'(t)=y''(t)=t*exp(t)-t+2*y'-y =t*exp(t)-t+2*u2(t)-u1(t) a2 = 0; b2 = 1; h2 = .1; ival2 = [0;0]; gfun = inline( '[y(2);t*exp(t)-t+2*y(2)-y(1)]' , 't' , 'y' ); gact = inline( '1/6*t^3*exp(t)-t*exp(t)+2*exp(t)-t-2' , 't' ); [t2,twoa] = rk4(gfun,a2,b2,h2,ival2);
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This note was uploaded on 09/19/2009 for the course MATH numerical taught by Professor Ford during the Spring '09 term at FAU.

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hw17_derek_rampal - Derek Rampal HW 17 17 10/20 5.7 232...

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