Legendre polynomials approximation method for solving Volterra integral equations of the first kind with discontinuous kernels

The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gausstype quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation method.

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Legendre polynomials approximation method for solving Volterra integral equations of the first kind with discontinuous kernels

Cited by 2 publications

References 21 publications

Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method

Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method

Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind

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