Homotopy perturbation method and Chebyshev polynomials for solving a class of singular and hypersingular integral equations. (English) Zbl 1405.65166
Summary: TIn this note, we review homotopy perturbation method (HPM), Discrete HPM, Chebyshev polynomials and its properties. Moreover, the convergences of HPM and error term of Chebyshev polynomials were discussed. Then, linear singular integral equations (SIEs) and hyper-singular integral equations (HSIEs) are solved by combining modified HPM together with Chebyshev polynomials. Convergences of the mixed method for the linear HSIEs are also obtained. Finally, illustrative examples and comparisons with different methods are presented.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E05 | Integral equations with kernels of Cauchy type |
| 42A10 | Trigonometric approximation |
| 65D30 | Numerical integration |
Keywords:
homotopy perturbation method (HPM); Gauss quadrature formula; nonlinear operator; singular integral equation; hyper-singular integralReferences:
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