scholarly journals A Wavelet Collocation Method for the Numerical Solution of Partial Differential Equations

1996 ◽  
Vol 3 (1) ◽  
pp. 1-9 ◽  
Author(s):  
S. Bertoluzza ◽  
G. Naldi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Partial Differential ◽  
Wavelet Collocation Method

Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method

2016 ◽  
Vol 10 (02) ◽  
pp. 1750026 ◽  
Author(s):  
S. C. Shiralashetti ◽  
L. M. Angadi ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Parabolic Partial Differential Equations ◽  
Test Problems ◽  
Parabolic Pdes ◽  
Partial Differential ◽  
Wavelet Collocation Method

In this paper, we applied the adaptive grid Haar wavelet collocation method (AGHWCM) for the numerical solution of parabolic partial differential equations (PDEs). The approach of AGHWCM for the numerical solution of parabolic PDEs is mentioned, the obtained numerical results, error analysis are presented in figures and tables. This shows that, the AGHWCM gives better accuracy than the HWCM and FDM. Some of the test problems are taken for demonstrating the validity and applicability of the AGHWCM.

scholarly journals A reliable algorithm to compute the approximate solution of KdV-type partial differential equations of order seven

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0244027
Author(s):  
Sidra Saleem ◽  
Malik Zawwar Hussain ◽  
Imran Aziz
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Approximate Solutions ◽  
Haar Wavelet ◽  
Partial Differential ◽  
Lax Equation ◽  
One Dimensional ◽  
Wavelet Collocation Method

The approximate solution of KdV-type partial differential equations of order seven is presented. The algorithm based on one-dimensional Haar wavelet collocation method is adapted for this purpose. One-dimensional Haar wavelet collocation method is verified on Lax equation, Sawada-Kotera-Ito equation and Kaup-Kuperschmidt equation of order seven. The approximated results are displayed by means of tables (consisting point wise errors and maximum absolute errors) to measure the accuracy and proficiency of the scheme in a few number of grid points. Moreover, the approximate solutions and exact solutions are compared graphically, that represent a close match between the two solutions and confirm the adequate behavior of the proposed method.

scholarly journals Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Hongchun Wu ◽  
Yulan Wang ◽  
Wei Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Present Method ◽  
Nonlinear Partial Differential Equations ◽  
Economic Systems ◽  
Partial Differential ◽  
Barycentric Interpolation ◽  
Chemical Cycling

Partial differential equations (PDEs) are widely used in mechanics, control processes, ecological and economic systems, chemical cycling systems, and epidemiology. Although there are some numerical methods for solving PDEs, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, we give the meshless barycentric interpolation collocation method (MBICM) for solving a class of PDEs. Four numerical experiments are carried out and compared with other methods; the accuracy of the numerical solution obtained by the present method is obviously improved.

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