Chebyshev Polynomial Based Numerical Inverse Laplace Transform Solutions of Linear Volterra Integral and Integro-Differential Equations
Department of Mathematics, Sant Longowal Institute of Engg. & Tech, Longowal (Punjab)
Abstract
There are enormous occasions when the methods for finding solutions of integral and integrodifferential equations lead to failure because of difficulty in inverting Laplace transform by standard technique.
Numerically inverting Laplace transform is cost effective in comparison to rather complicated technique of complex analysis. In the process of numerical inversion, an odd cosine series which is ultimately based on Chebyshev
polynomial has been used. The adequacy of method is illustrated through numerical examples of convolution type
linear Volterra integral equations of second kind which include weakly singular Abel's integral equation and Volterra integro-differential equation.
