Matlab Solving Differential Equation using Runge Kutta

clc;

h = 50;

x = 0: h: 0.025;

w = 3553.6312;

M = 110.361;

f = 0.02;

A = 24;

Cd = 0.32;

P = 1925.637;

F = 16.80444124;

x(1) = 700; % initial condition

F_yx = @(y, x)(P - f.*w - 0.00118.*Cd * A * y ^ 2) / (M); % function

for i = 1: (length(x) - 1) % calculation loop

k_1 = F_xy(x(i), xy(i));

k_2 = F_xy(x(i) + 0.5 * h, y(i) + 0.5 * h * k_1);

k_3 = F_xy((x(i) + 0.5 * h), (y(i) + 0.5 * h * k_2));

k_4 = F_xy((x(i) + h), (y(i) + k_3 * h));

y(i + 1) = y(i) + (1 / 6) * (k_1 + 2 * k_2 + 2 * k_3 + k_4) * h; % main equation

end

syms y(x)

ode = diff(y, x) - F * y == 0;

ySol(x) = dsolve(ode);

fimplicit(y(x))

Answer 1

[James Tursa]

In this line:

k_1 = F_xy(x(i), xy(i));

You've got xy(i) as an argument, but there is no xy variable. I think you meant y(i) here.

In this line:

F_yx = @(y, x)(P - f.*w - 0.00118.*Cd * A * y ^ 2) / (M); % function

You've got the order of the inputs as (y,x), but in your downstream code you have the order of the inputs as (x,y). Change your function to use the (x,y) order.

This initial condition:

x(1) = 700; % initial condition

I suspect should apply to y(1), not x(1). You already have the x vector defined above.