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Numerical solutions for second-kind Volterra integral equations by Galerkin methods

Shu Hua Zhang, Yan Ping Lin, Ming Rao (2000)

Applications of Mathematics

In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...

Numerical solutions to integral equations equivalent to differential equations with fractional time

Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej (2010)

International Journal of Applied Mathematics and Computer Science

This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.

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