Hermitian Methods for the Approximate Solution of Partial Differential Equations

1970 ◽  
Vol 6 (4) ◽  
pp. 365-374 ◽  
Author(s):  
J. G. A. CROLL
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

scholarly journals Sparse approximate solution of partial differential equations

2010 ◽  
Vol 60 (4) ◽  
pp. 452-472 ◽  
Author(s):  
Sadegh Jokar ◽  
Volker Mehrmann ◽  
Marc E. Pfetsch ◽  
Harry Yserentant
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

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 TECHNIQUE FOR APPROXIMATE SOLUTION OF FRACTIONAL-ORDER PARTIAL DIFFERENTIAL EQUATIONS

Fractals ◽  
2021 ◽  
Author(s):  
LAIQ ZADA ◽  
RASHID NAWAZ ◽  
MOHAMMAD A. ALQUDAH ◽  
KOTTAKKARAN SOOPPY NISAR
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Auxiliary Function ◽  
Partial Differential ◽  
Convergence Control ◽  
A New Technique ◽  
Fifth Order ◽  
First Time

In the present paper, the optimal auxiliary function method (OAFM) has been extended for the first time to fractional-order partial differential equations (FPDEs) with convergence analysis. To find the accuracy of the OAFM, we consider the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations as a test example. The proposed technique has auxiliary functions and convergence control parameters, which accelerate the convergence of the method. The other advantage of this method is that there is no need for a small or large parameter assumption, and it gives an approximate solution after only one iteration. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different FPDEs.

scholarly journals On a New Modification of Homotopy Analysis Method for Solving Nonlinear Nonhomogeneous Differential Equations

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Shaheed N. Huseen ◽  
Haider A. Mkharrib
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
New Technique ◽  
Analysis Method ◽  
Partial Differential ◽  
Analysis Technique ◽  
Homotopy Analysis

In this paper, new powerful modification of homotopy analysis technique (NMHAM) was submitted to create an approximate solution of nonhomogeneous nonlinear ordinary and partial differential equations. The NMHAM is a combination of the new technique of homotopy analysis method(NHAM) [4] and the new technique of homotopy analysis method(nHAM) [7].Three illustrative examples are employed to illustrate the accuracy and computational proficiency of this approach. The outcomes uncover that the NMHAM is more accurate than the NHAM and nHAM.

Approximate solution of time-fractional fuzzy partial differential equations

2019 ◽  
Vol 38 (1) ◽  
Author(s):  
Mehmet Senol ◽  
Sevda Atpinar ◽  
Zarife Zararsiz ◽  
Soheil Salahshour ◽  
Ali Ahmadian
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

scholarly journals A Stable Difference Scheme for a Third-Order Partial Differential Equation

2018 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
A Ashyralyev ◽  
Kh Belakroum
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Nonlocal Boundary ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space H with a self-adjoint positive definite operator A is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for oneand two-dimensional third order partial differential equations are provided.

Sign in / Sign up

Export Citation Format

Share Document