Does anyone know how to fix this?

I'm using forward differencing to estimate a differential equation, but my estimation isn't accounting for my boundary value y(10)=0

%cleanup

clc

clear

clf

%variables and setup

q = -0.6

EI = 1900

L = 10

%Analytical Solution and plot

f = @(x) (q*x.*(L.^3-2*L*x.^2+x.^3))/(24*EI)

x_exact = linspace(0,L)

y_exact = f(x_exact)

figure(1)

hold on

plot(x_exact,y_exact)

%Numerical Solution and Plot

dx = input('Input delta x value: ')

N = (L/dx)+1

y(1) = 0

y(L+1) = 0

y(10) = 0

x(1) = 0

x(2) = dx

C = (q*dx^2)/(2*EI)

for (i=2:N-1)

x(i+1) = x(i) + dx

y(i+1) = C*(x(i)*(x(i)-L))+2*y(i)-y(i-1)

i = i+1

end

plot(x,y)

title('Deflection vs. Position')

xlabel('X')

ylabel('Deflection')

legend('Exact Solution', 'Forward Differencing','Location','NorthWest')

[Ridwan Alam]

Can you please share the code using the 'code editor'?

Answer 1

[Ridwan Alam]

y(10) referes to the 10th element of the array y; not necessarily the value of y when x=10 or the last array element. to assign the last element of y, you can use the length of y (N) to initialize: y(N)=0 or y(length(y_exact))=0;

is your increment of i [i = i+1] intentional inside the for loop? also, the for loop runs upto i=N-1, then y(i+1)=y(N)=whatever is calculated by your equation and it overwrites your initial assignment.

a forward differencing doesn't use the end boundary value in estimating.