Using the substitution reduce the equation:
to Bessel’s equation. Hence find its solution.
To reduce the given differential equation to Bessel's equation, we make the substitution z = sqrt{x}. Then, we have:
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If is approximated by:
find the values of a and b. What is the order of approximation?
Construct Green’s function for the following boundary value problem:
with y(0) = y(1) = 0.
Prove that
Evaluate , using convolution theorem.
Using Laplace transform, solve the p.d.e.:
subject to the conditions:
Determine an appropriate Green’s function either by using the method of variation of parameters or otherwise, for the following boundary value problem:
Heat conduction equation is approximated by the method:
Find the order of the method and investigate the stability of this method using Von Neumann method.