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

2017 ◽  
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

scholarly journals Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ishfaq Ahmad Ganaie ◽  
Shelly Arora ◽  
V. K. Kukreja
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Spline Method ◽  
Orthogonal Collocation ◽  
Nonlinear Boundary Value Problems ◽  
B Spline ◽  
Linear And Nonlinear ◽  
Volume Method

Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.

scholarly journals Numerical solutions of higher order boundary value problems via wavelet approach

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shams Ul Arifeen ◽  
Sirajul Haq ◽  
Abdul Ghafoor ◽  
Asad Ullah ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Linear Equations ◽  
Haar Wavelet ◽  
Higher Order ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Resolution Level ◽  
Linear And Nonlinear

AbstractThis paper presents a numerical scheme based on Haar wavelet for the solutions of higher order linear and nonlinear boundary value problems. In nonlinear cases, quasilinearization has been applied to deal with nonlinearity. Then, through collocation approach computing solutions of boundary value problems reduces to solve a system of linear equations which are computationally easy. The performance of the proposed technique is portrayed on some linear and nonlinear test problems including tenth, twelfth, and thirteen orders. Further convergence of the proposed method is investigated via asymptotic expansion. Moreover, computed results have been matched with the existing results, which shows that our results are comparably better. It is observed from convergence theoretically and verified computationally that by increasing the resolution level the accuracy also increases.

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

2016 ◽  
Vol 05 (02) ◽  
pp. 1650010 ◽  
Author(s):  
S. C. Shiralashetti ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Fluid Dynamics ◽  
Differential Equations ◽  
Error Analysis ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Elastohydrodynamic Lubrication ◽  
Haar Wavelet ◽  
Nonlinear Boundary Value Problems

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.

scholarly journals Efficient Numerical Scheme for the Solution of Tenth Order Boundary Value Problems by the Haar Wavelet Method

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1874
Author(s):  
Rohul Amin ◽  
Kamal Shah ◽  
Imran Khan ◽  
Muhammad Asif ◽  
Mehdi Salimi ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Haar Wavelet ◽  
Nonlinear Boundary Value Problems ◽  
Haar Functions ◽  
Collocation Points ◽  
Wavelet Collocation Method ◽  
Mean Square Errors ◽  
Gauss Points

In this paper, an accurate and fast algorithm is developed for the solution of tenth order boundary value problems. The Haar wavelet collocation method is applied to both linear and nonlinear boundary value problems. In this technqiue, the tenth order derivative in boundary value problem is approximated using Haar functions and the process of integration is used to obtain the expression of lower order derivatives and approximate solution for the unknown function. Three linear and two nonlinear examples are taken from literature for checking validation and the convergence of the proposed technique. The maximum absolute and root mean square errors are compared with the exact solution at different collocation and Gauss points. The experimental rate of convergence using different number of collocation points is also calculated, which is nearly equal to 2.

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