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Physicists Hermite wavelet method for singular differential equations. (English) Zbl 1360.34052

Summary: This manuscript witnesses a modification in the Legendre Wavelet Method (LWM) by inserting Physicists Hermite Polynomials instead of the traditional Legendre’s Polynomials. The modified version which is called the Physicists Hermite Wavelet Method (PHWM) is highly accurate and is tested on Singular Differential Equations (SDEs). Five examples are given to elucidate the solution procedure. Comparison of numerical results explicitly reflects the very high level of accuracy.

MSC:

34B16 Singular nonlinear boundary value problems for ordinary differential equations
65T60 Numerical methods for wavelets
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

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