Solving Some Oscillatory Problems using Adomian Decomposition Method and Haar Wavelet Method

In this work, authors obtained the series solution of nonlinear fractional partial differential equations, which is emerging in a spatial diffusion of biological population model using Elzaki transform homotopy perturbation method (ETHPM). The Elzaki transform homotopy perturbation method is a combined form of the Elzaki transform and homotopy perturbation method. Three test illustrations are used to show the proficiency and accuracy of the projected method. It has been observed that the proposed technique can be widely employed to examine other real world problems. The results obtained with the help of the proposed technique are plotted for different fractional orders.

Section: Elzaki Transform Homotopy Perturbation Methods (Ethpm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Reliable Computational Algorithm for Solving Fractional Biological Population Model

Devi

Jakhar

2021

“…But now that powerful software and contemporary computers have been developed, it is possible to use analytical or numerical methods to solve these issues [1]. Recently, methods have been utilized to solve partial differential equations, both linear and nonlinear, numerically and analytically, for instance, Hermite polynomials [2], a comprehensive approximation system based on biorthogonal wavelets [3], the Adomian Decomposition Method and Haar Wavelet Method [4] etc.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Cahn-Allen Equations by Wavelet Based Lifting Schemes

Angadi

2024

The Cahn-Allen equation is a reaction-diffusion equation of mathematical physics that describes the process of phase separation in multi-component alloy systems and order-disorder transitions. This paper presented a numerical solution of Cahn-Allen equations by Lifting scheme using different wavelet filter coefficients. The numerical results obtained using this scheme are compared with the exact solution to demonstrate the accuracy and fast convergence in less computational time than the existing scheme. Some problems are taken to show the validity and applicability of the scheme.

“…Hwang and Ryoo [10] investigate the structure and symmetry of zeros of the two variable degenerate Hermite equations. Singh [11] presented two numerical techniques such as Adomian decomposition and Haar wavelet methods for solving some oscillatory problems arising in several applications of science and engineering. Numerically investigation of the non-Newtonian viscoelastic Oldroyd-B fluid flows in two-dimensional rectangular domain has been discussed by Helal [12].…”

Section: Introductionmentioning

confidence: 99%

Solving Some Differential Equations Arising in Electric Engineering Using Hermite Polynomials

Singh¹,

Singh²

2020

Self Cite

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the electric circuit equations arising in many branches of sciences and engineering. By using collocation points and Hermite polynomials, electric circuit equations are transformed into a system of linear algebraic equations with unknown Hermite coefficients. These unknown Hermite coefficients have been computed by solving such algebraic equations. To illustrate the accuracy of the proposed method some numerical examples are presented.