Haar wavelet based numerical solution of nonlinear differential equations arising in fluid dynamics

In this paper, we obtained the Haar wavelet-based numerical solution of the nonlinear differential equations arising in fluid dynamics, i.e., electrohydrodynamic flow, elastohydrodynamic lubrication and nonlinear boundary value problems. Error analysis is observed, it shows that the Haar wavelet-based results give better accuracy than the existing methods, which is justified through illustrative examples.

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Solution of Third Order Linear and Nonlinear Boundary Value Problems of Integro-Differential Equations Using Haar Wavelet Method

Results in Physics ◽

10.1016/j.rinp.2021.104176 ◽

2021 ◽

pp. 104176

Author(s):

M.M. Alqarni ◽

Rohul Amin ◽

Kamal Shah ◽

Shah Nazir ◽

Muhammad Awais ◽

...

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Nonlinear Boundary ◽

Haar Wavelet ◽

Nonlinear Boundary Value Problems ◽

Third Order ◽

Wavelet Method ◽

Haar Wavelet Method ◽

Order Linear ◽

Linear And Nonlinear

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Numerical solution by Haar wavelet collocation method for a class of higher order linear and nonlinear boundary value problems

10.1063/1.4990337 ◽

2017 ◽

Cited By ~ 1

Author(s):

Ratesh Kumar ◽

Harpreet Kaur ◽

Geeta Arora

Keyword(s):

Numerical Solution ◽

Boundary Value Problems ◽

Collocation Method ◽

Nonlinear Boundary ◽

Haar Wavelet ◽

Higher Order ◽

Nonlinear Boundary Value Problems ◽

Order Linear ◽

Wavelet Collocation Method ◽

Linear And Nonlinear

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Fractional boundary value problems: Analysis and numerical methods

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-011-0034-4 ◽

2011 ◽

Vol 14 (4) ◽

Cited By ~ 32

Author(s):

Neville Ford ◽

M. Morgado

Keyword(s):

Numerical Methods ◽

Differential Equations ◽

Numerical Solution ◽

Boundary Value Problems ◽

Existence And Uniqueness ◽

Nonlinear Boundary ◽

Boundary Value ◽

Nonlinear Boundary Value Problems ◽

Uniqueness Of The Solution ◽

Fractional Boundary Value Problems

AbstractIn this paper we consider nonlinear boundary value problems for differential equations of fractional order α, 0 < α < 1. We study the existence and uniqueness of the solution and extend existing published results. In the last part of the paper we study a class of prototype methods to determine their numerical solution.

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A NEW ALGORITHM FOR SOLVING NONLINEAR BOUNDARY VALUE PROBLEMS ARISING IN HEAT TRANSFER

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962311000499 ◽

2011 ◽

Vol 02 (03) ◽

pp. 355-373 ◽

Cited By ~ 13

Author(s):

S. S. MOTSA

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Closed Form ◽

Boundary Value Problems ◽

Nonlinear Equations ◽

Nonlinear Boundary ◽

Numerical Solutions ◽

Nonlinear Differential Equations ◽

Analytic Solutions ◽

Nonlinear Boundary Value Problems

In this paper, a very efficient and easy-to-use successive linearization approach for solving nonlinear differential equations is proposed. The implementation of the method is demonstrated by solving three nonlinear differential equations of different complexities arising in heat transfer. New closed form explicit analytic solutions of some of the governing nonlinear equations are obtained and compared with the results of the proposed method and with numerical solutions from the MATLAB in-built routine bvp4c.

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