The Petrov-Galerkin Method and Chebyshev Multiwavelet Basis for Solving Integro-Differential Equations

There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For numerical examples, the solutions may be produced with good accuracy, by choosing suitable trial and test spaces in Petrov-Galerkin method.