i want to solve the partial differential equation
A*y(x,t)'''' + B*d²y(x,t)/dt² + C*dy(x,t)/dt + D*y(x,t) = I(x,t)
' means derivation in respect to x
dt means derivation in respect to t

A,B,C,D are real constants

The input I(x,t) is given as an array I[m][n] which is read in from a file.

I dont know any numerical method to solve this problem. I heard of the finite difference method which is very practicable to solve such problem but i dont know how to applicate it on this equation.

Maybe someone might help me to get forward.

ps. please excuse my horrible english

Thanx to all!

Use a Taylor series expansion for y(x,t) to find values of the function at x+2*a, x+a, x-a and x-2*a so that

y(x+a) = y(x) + a*y'(x) + a/2*y''(x) + ... + a^5/120*y'''''(x) + O(a^6),

etc. (I have omitted the variable t)

find expressions for y''''(x) and y''(x) from these four equations, and eliminate y''(x). If we move to discrete variables so that (x+a) = (j+1)*dx (i.e. a = dx), we find y''''(x) is approximated by

12*(y[j+2]-4*y[j+1]+6*y[j]-4*y[j-1]+y[j-2])/(5*a^4)

to order a^2.

Other differencing schemes are given in the NR books. Hope this helps