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Haar Wavelet Method for Solving Some Nonlinear Parabolic Equations

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Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

Abstract

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this chapter, we develop an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations. The equations include the Newell–Whitehead equation, Cahn–Allen equation, FitzHugh–Nagumo equation, Fisher’s equation, Burgers’ equation, and the Burgers–Fisher equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover, the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs, and computationally attractive.

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Authors and Affiliations

  1. School of Arts Science and Humanities (SASH), SASTRA Deemed to be University, Thanjavur, Tamil Nadu, India

    G. Hariharan

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  1. G. Hariharan
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Correspondence to G. Hariharan .

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Hariharan, G. (2019). Haar Wavelet Method for Solving Some Nonlinear Parabolic Equations. In: Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-32-9960-3_7

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