Abstract:
In this work, a class of spectral based computational method for the solution of partial
differential equation is developed. Theoretical solution to a given general second order partial
differential equation is partly differentiated at constant time t but varying on the space (x) and
substituted to the aforementioned equation; leading to a general parabolic partial differential
equation and; by adopting the above spectral based theoretical solution to this general
parabolic equation and further simplifications were performed resulting into development of a
class of spectral based computational methods for solution of partial differential equations at
step numbers j = 2, 3, and 4, respectively. Nine distinct spectral based new computational
schemes were obtained. The accuracy, consistency, stability and convergence properties of
these methods were determined. The methods are implemented on some sampled problems
that involve both constant and, variable coefficients parabolic partial differential equations;
and evaluated by comparing them with some existing difference methods. The results
obtained are found to be more rapidly converging as the step lengths h and k approaches
zeros. This work provided accurate numerical solutions to a class of dynamical problems
having time dependent boundary conditions. Higher ordered parabolic partial differential
equations with defined theoretical solutions and given boundary conditions can be solved
directly using any of these methods which amount to no time wastage, reduction of
antiqueness and expenses.
