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A new modification of the homotopy perturbation method for linear and nonlinear operators. (English) Zbl 1122.65092
Summary: We present an efficient modification of the homotopy perturbation method that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy perturbation method. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work. The new modification introduces a promising tool for many linear and nonlinear problems.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
35K55 Nonlinear parabolic equations
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
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