Find:
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Use Fourier transforms to solve the boundary value problem:
subject to the conditions:
i)
ii)
Using the generating function Jn(x), prove that Jn-1(x)+Jn+1(x)= (x), for integer values X of n.
Using method of Ferobenius, find the solution of the differential equation:
near x = 0.
Find the solution of = 0 in R subject to the boundary conditions:
where R is the square 0≤ x ≤1,0≤ y ≤1, using the five point formula. Use central difference approximation in the boundary condition. Assume uniform step length h = 1/2 along the axes.
Using second order finite difference method, solve the boundary value problem:
Using step length
Find the solution of the initial boundary value problem:
subject to given initial and boundary conditions:
You may use step length along x-axis, h = 2.0 and solve by Schmidt method with mesh ratio
Find the solution of the heat conduction equation subject to the given initial and boundary conditions:
Using Laasonen method with and .
Integrate for two levels.