MATLAB: Taylor and Euler Method for ODE

homework

y'-sin(4t)=0 y(0)=-0.25. 1. Use Taylor method to solve up to t4 for 20 steps, h=0.1.

Best Answer

MATLAB is a 0-based indexing language. So you can't have y(0) in your code. It will need to start at y(1).

y(1)= -0.25;

Also, you need to index into your t vector as t(i):

    Dy(i)=sin(4*t(i));

Related Solutions

MATLAB: Using ode 45 to estimate the derivative

ode=@(t, x) [x(2) ; -(1/t)*x(1)];
[t, x] = ode45(ode, [-1, 3], [0, 2]);
y=x(:,1)
dy=x(:,2)
out=dy(3)

MATLAB: I’m trying to do a Taylor series method for the equation y and compare it to the analytical solution. However, I keep getting a matrix dimension error. any help would be much appreciated.

Using diff reduces the dimension of the array by 1. You check the dimensions of y1, y2, y3, y4..they are of size 1X20, 1X19, 1x18, 1x17 respectively. Instead of suing diff you can striaght away use the differentiation of y.

t = 0:0.1:2; %h = 0.1%
h = 0.1;
y = (-cos(4*t))./4 - 0.5; 
z = (-cos(0))./4 - 0.5;
 
y1 =  4*sin(4*t) ;
y2 = 16*cos(4*t) ;
y3 = -64*sin(4*t) ;
y4 = 256*cos(4*t) ;
 
taylor_y = (z + h*y1 + ((h^2/factorial(2))*y2) + ((h^3/factorial(3))*y3) + ((h^4/factorial(4))*y4));
fig = figure();
set(fig,'color','white');
plot(t,y,'LineWidth',2)
grid on
xlabel('t')
ylabel('y')
hold on
plot(t,taylor_y,'r','LineWidth',2)

Best Answer

Related Solutions

MATLAB: Using ode 45 to estimate the derivative

MATLAB: I’m trying to do a Taylor series method for the equation y and compare it to the analytical solution. However, I keep getting a matrix dimension error. any help would be much appreciated.

Related Question