SOLVING NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS USING AN ACCURATE SPECTRAL COLLOCATION METHOD
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Date
2021
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Publisher
Université de M'sila
Abstract
In this paper, we present a Jacobi spectral collocation method
to solve nonlinear Volterra-Fredholm integral equations with smooth kernels.
The main idea in this approach is to convert the original problem into an equivalent
one through appropriate variable transformations so that the resulting
equation can be accurately solved using spectral collocation at the Jacobi-Gauss
points. The convergence and error analysis are discussed for both L∞ and weighted
L2 norms. We confirm the theoretical prediction of the exponential rate of convergence
by the numerical results which are compared with well-known methods.