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Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

F. Talay Akyildiz

F. Talay Akyildiz

Department of Mathematics and Statistics, Faculty of Science, Al-Imam UniversityRiyadh, Saudi Arabia
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Talay Akyildiz, F.
 and 
K. Vajravelu

K. Vajravelu

Department of Mathematics, University of Central FloridaOrlando, USA
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Vajravelu, K.
  
Oct 03, 2018
Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order's Cover Image
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Published Online: Oct 03, 2018
Page range: 255 - 264
Received: Mar 23, 2018
Accepted: Jun 08, 2018
DOI: https://doi.org/10.21042/AMNS.2018.1.00019
Keywords
© 2018 F. Talay Akyildiz and K. Vajravelu, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

First three approximation for time variable.
First three approximation for time variable.

Fig. 2

Centerline electrostatic potential (a) t = 0.05(line) (b) t = 0.5(point) (c) t = 2.5(polygon.)
Centerline electrostatic potential (a) t = 0.05(line) (b) t = 0.5(point) (c) t = 2.5(polygon.)

Fig. 3

Solution of NPB equation at t = 2.5.
Solution of NPB equation at t = 2.5.

Fig. 4

Approximation to the Source function in terms of the base Function at t = 1 for (N = 8), Green line is the source function and red line(dotted line) approximation.
Approximation to the Source function in terms of the base Function at t = 1 for (N = 8), Green line is the source function and red line(dotted line) approximation.

Fig. 5

Lw2$\begin{array}{} L^{2}_{w} \end{array}$error for test problem 2 at t=1.
Lw2$\begin{array}{} L^{2}_{w} \end{array}$error for test problem 2 at t=1.
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