Solution of third-order Emden–Fowler-type equations using wavelet methods

Abstract

Purpose The numerical solution of third-order boundary value problems (BVPs) has a great importance because of their applications in fluid dynamics, aerodynamics, astrophysics, nuclear reactions, rocket science etc. The purpose of this paper is to develop two computational methods based on Hermite wavelet and Bernoulli wavelet for the solution of third-order initial/BVPs. Design/methodology/approach Because of the presence of singularity and the strong nonlinear nature, most of third-order BVPs do not occupy exact solution. Therefore, numerical techniques play an important role for the solution of such type of third-order BVPs. The proposed methods convert third-order BVPs into a system of algebraic equations, and on solving them, approximate solution is obtained. Finally, the numerical simulation has been done to validate the reliability and accuracy of developed methods. Findings This paper discussed the solution of linear, nonlinear, nonlinear singular (Emden–Fowler type) and self-adjoint singularly perturbed singular (generalized Emden–Fowler type) third-order BVPs using wavelets. A comparison of the results of proposed methods with the results of existing methods has been given. The proposed methods give the accuracy up to 19 decimal places as the resolution level is increased. Originality/value This paper is one of the first in the literature that investigates the solution of third-order Emden–Fowler-type equations using Bernoulli and Hermite wavelets. This paper also discusses the error bounds of the proposed methods for the stability of approximate solutions.

A collocation method for time‐fractional diffusion equation on a metric star graph with η$$ \eta $$ edges

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An efficient collocation algorithm for third order non-linear Emden–Fowler equation with multi-singularity

“…Recently, Swati et al [2] solve the third order EFSDE by applying uniform Haar wavelet collocation algorithm. In [25], the authors developed numerical algorithm by using wavelets for third-order non-linear boundary value problems. Also, Verma and Kumar [26], solve the third order EFSDE by applying the artificial neural network technique.…”

Comprehensive review of numerical schemes based on Hermite wavelets

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