Higher resolution methods based on quasilinearization and Haar wavelets on Lane–Emden equations

2019 ◽  
Vol 17 (03) ◽  
pp. 1950005 ◽  
Author(s):  
Amit K. Verma ◽  
Diksha Tiwari
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Research Paper ◽  
Haar Wavelets ◽  
Singular Differential Equations ◽  
Wavelet Collocation Method

Computing solutions of singular differential equations has always been a challenge as near the point of singularity it is extremely difficult to capture the solution. In this research paper, Haar wavelet coupled with quasilinearization approach (HWQA) is proposed for computing numerical solution of nonlinear SBVPs popularly also referred as Lane–Emden equations. This technique is the combination of quasilinearization and Haar wavelet collocation method. To show the accuracy of the HWQA, several examples are presented. Convergence of the proposed method is also established in this paper, which shows that proposed method converges very fast.

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 A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 545 ◽  
Author(s):  
M. Motawi Khashan ◽  
Rohul Amin ◽  
Muhammed I. Syam
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Test Problem ◽  
Fractional Derivatives ◽  
Haar Wavelet ◽  
Integer Order ◽  
Error Functions ◽  
Nodal Points ◽  
Estimated Error

In this paper, a new collocation method based on Haar wavelet is developed for numerical solution of Riccati type differential equations with non-integer order. The fractional derivatives are considered in the Caputo sense. The method is applied to one test problem. The maximum absolute estimated error functions are calculated, and the performance of the process is demonstrated by calculating the maximum absolute estimated error functions for a distinct number of nodal points. The results show that the method is applicable and efficient.

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

2017 ◽  
Vol 18 ◽  
pp. 50-59 ◽  
Author(s):  
S.C. Shiralashetti ◽  
R.A. Mundewadi
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Wavelet Collocation Method

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

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