Not enough input arguments.

Not enough input arguments.

Error in BDF>@(t,y)mu*(y-cos(t))-sin(t) (line 7)

f_m = @(t,y) mu*(y-cos(t))-sin(t);

Error in BDF (line 14)

y_m(i)=(4.*y_m(i-1)-y_m(i-2))/3+(2/3).*h*(3*f_m(t(i)))

%% Backward Difference Formula Method %%
clc; clear all;
h=0.01;
t=0:h:1;
n=numel(t);
mu = 20;
f_m = @(t,y) mu*(y-cos(t))-sin(t);
exact = @(t) exp(mu*t)+cos(t);
%initials%
y_m(1)=exact(0);
y_m(2)=exact(h);
%Adam-Bashforth method%
for i=3:n
    y_m(i)=(4.*y_m(i-1)-y_m(i-2))/3+(2/3).*h*(3*f_m(t(i)))
end

plot(t, exact(t)); 
hold
plot(t,y);
%plot(t,y,'-o');
legend('Exact Solution','BDF Solution')
xlabel('t')
ylabel('y')
title('When h = 0.01 and µ=20')

[Hazel Can]

@Lateef Adewale Kareem Would this kind of code be correct for the BDF method?

[Torsten]

The BDF method gives the following equation for y(n):

y(n) = ( 4*y(n-1)-y(n-2) )/3 + 2*h/3* ( mu*( y(n) - cos(t(n)) ) - sin(t(n)) ) 

Solve this equation for y(n) and update y_m(i) in the loop accordingly.

[Hazel Can]

I didnt understand. How exactly do I do this?

[Torsten]

If I write

x = ( 4*y(n-1)-y(n-2) )/3 + 2*h/3* ( mu*( x - cos(t(n)) ) - sin(t(n)) )

and say to solve for x, do you know how to proceed ?

After doing this, your loop looks like

for i=3:n
    y_m(i) = the expression you got for x (with y(...) replaced by y_m(...))
end

[Hazel Can]

i dont know how i use the 'solve command' :(

[Hazel Can]

This code piece can not work correctly without errors.

%Adam-Bashforth method%

x = ( 4*y_m(n-1)-y_m(n-2) )/3 + 2*h/3* ( mu*( x - cos(t(n)) ) - sin(t(n)) )

S=solve(x)

for i=3:n

y_m(i)=(4.*y_m(i-1)-y_m(i-2))/3+(2/3).*h*(3*f_m(t(i)))

end

Answer 1

[Jan]

f_m = @(t,y) mu*(y-cos(t))-sin(t);

f_m is a function with 2 inputs.

y_m(i)=(4.*y_m(i-1)-y_m(i-2))/3+(2/3).*h*(3*f_m(t(i)))
%                                               ^^^^

Here you provide 1 input only.

[Hazel Can]

How can i fix this ?

Answer 2

[Lateef Adewale Kareem]

%% Backward Difference Formula Method %%
clc; clear all;
h=0.01;
t=0:h:1;
n=numel(t);
mu = 20;
f_m = @(t,y) mu*(y-cos(t))-sin(t);
exact = @(t) exp(mu*t)+cos(t);
%initials%
y_m(1)=exact(0);
y_m(2)=exact(h);
%Adam-Bashforth method%
for i=3:n
    fun = @(x) x - (4*y_m(i-1)-y_m(i-2))/3 - 2*h/3*f_m(t(i), x);
    y_m(i)=fzero(fun, y_m(i-1));
end
plot(t, exact(t)); hold

Current plot held

plot(t,y_m);
%plot(t,y,'-o');
legend('Exact Solution','BDF Solution')
xlabel('t')
ylabel('y')
title('When h = 0.01 and µ=20')