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Ingy döt Net 2023-07-01 11:58:00 -04:00
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commit cb5bb5e222
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Task/Runge-Kutta-method/MATLAB/runge-kutta-method.m Normal file
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function testRK4Programs
figure
hold on
t = 0:0.1:10;
y = 0.0625.*(t.^2+4).^2;
plot(t, y, '-k')
[tode4, yode4] = testODE4(t);
plot(tode4, yode4, '--b')
[trk4, yrk4] = testRK4(t);
plot(trk4, yrk4, ':r')
legend('Exact', 'ODE4', 'RK4')
hold off
fprintf('Time\tExactVal\tODE4Val\tODE4Error\tRK4Val\tRK4Error\n')
for k = 1:10:length(t)
fprintf('%.f\t\t%7.3f\t\t%7.3f\t%7.3g\t%7.3f\t%7.3g\n', t(k), y(k), ...
yode4(k), abs(y(k)-yode4(k)), yrk4(k), abs(y(k)-yrk4(k)))
end
end
function [t, y] = testODE4(t)
y0 = 1;
y = ode4(@(tVal,yVal)tVal*sqrt(yVal), t, y0);
end
function [t, y] = testRK4(t)
dydt = @(tVal,yVal)tVal*sqrt(yVal);
y = zeros(size(t));
y(1) = 1;
for k = 1:length(t)-1
dt = t(k+1)-t(k);
dy1 = dt*dydt(t(k), y(k));
dy2 = dt*dydt(t(k)+0.5*dt, y(k)+0.5*dy1);
dy3 = dt*dydt(t(k)+0.5*dt, y(k)+0.5*dy2);
dy4 = dt*dydt(t(k)+dt, y(k)+dy3);
y(k+1) = y(k)+(dy1+2*dy2+2*dy3+dy4)/6;
end
end