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.