Displaying similar documents to “Numerical solutions for second-kind Volterra integral equations by Galerkin methods”

Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations

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

Applications of Mathematics

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We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods...

Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type

Babak Shiri, Sedaghat Shahmorad, Gholamreza Hojjati (2013)

International Journal of Applied Mathematics and Computer Science

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In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical...