scholarly journals Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 770-778 ◽  
Author(s):  
Mohamed A. Abdelkawy ◽  
Zulqurnain Sabir ◽  
Juan L. G. Guirao ◽  
Tareq Saeed
Keyword(s):  
Collocation Method ◽  
Second Order ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Differential Model ◽  
Numerical Investigations ◽  
Present Technique ◽  
Functional Differential

AbstractThe present study aims to design a second-order nonlinear Lane–Emden coupled functional differential model and numerically investigate by using the famous spectral collocation method. For validation of the newly designed model, three dissimilar variants have been considered and formulated numerically by applying a famous spectral collocation method. Moreover, a comparison of the obtained results with the exact/true results endorses the effectiveness and competency of the newly designed model, as well as the present technique.

scholarly journals Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations

2019 ◽  
Vol 24 (3) ◽  
pp. 332-352 ◽  
Author(s):  
Eid H. Doha ◽  
Mohamed A. Abdelkawy ◽  
Ahmed Z.M. Amin ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Jacobi Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Shifted Jacobi Polynomials ◽  
Present Technique ◽  
Jacobi Spectral Collocation Method ◽  
The Given

This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

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