Weakly singular, singular and hypersingular integrals in 3-D elasticity and fracture mechanics
Journal of the Chinese Institute of Engineers - Special issue on boundary element methods—1
Homotopy perturbation method: a new nonlinear analytical technique
Applied Mathematics and Computation
SIAM Journal on Numerical Analysis
Spline collocation method for integro-differential equations with weakly singular kernels
Journal of Computational and Applied Mathematics
Hybrid collocation methods for Fredholm integral equations with weakly singular kernels
Applied Numerical Mathematics
Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Solution of delay differential equations via a homotopy perturbation method
Mathematical and Computer Modelling: An International Journal
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In this paper, an effective method based upon the piecewise homotopy perturbation method (PHPM) is proposed for finding the numerical solutions of Fredholm integro-differential equations with weakly singular kernels. For these equations, the traditional homotopy perturbation method is divergent. So we present a modified homotopy perturbation method for solving this kind of equation. The advantages of the approach of this paper lie in the feature that this technique not only achieves an approximate solution with high accuracy, but also improves the calculation speed. Two examples are given to show the effectiveness and convenience of this method.