| Citation: |
S. Kumbinarasaiah, Mustafa Inc, Hadi Rezazadeh, J. C. Umavathi. A NOVEL TECHNIQUE FOR SOLVING (2+1) DIMENSIONAL SYSTEM OF NONLINEAR COUPLED PARTIAL DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1890-1909. doi: 10.11948/20220279
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A NOVEL TECHNIQUE FOR SOLVING (2+1) DIMENSIONAL SYSTEM OF NONLINEAR COUPLED PARTIAL DIFFERENTIAL EQUATION
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Abstract
We present a highly efficient method to find numerical solutions to the system of PDEs. The method unifies the methods of collocation and Laguerre wavelet series (LWS). The system of (2+1)-dimensional PDEs is reduced to a set of equations having Laguerre wavelet coefficients (LWC). Computational examples are provided to validate the efficiency of the technique and we discussed the comparison between the present method and other methods solution with the exact solution. Computational results indicate that the present method is better than the other methods in the literature.
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References
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S. Kumbinarasaiah, Mustafa Inc, Hadi Rezazadeh, J. C. Umavathi. A NOVEL TECHNIQUE FOR SOLVING (2+1) DIMENSIONAL SYSTEM OF NONLINEAR COUPLED PARTIAL DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1890-1909. doi: 10.11948/20220279
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Figure 1.
Graphical representation of ns of
$ u(x, y, 0.01) $ $ u(x, y, 0.01) $ $ u(x, y, 0.01) $ $ M=2 $ $ u(x, y, 0.01) $ $ M=5 $ $ u(x, y, 0.01) $ $ M=2 $ -
Figure 2.
Graphical representation of ns of
$ u(x, y, 0.01) $ $ u(x, y, 0.01) $ $ u(x, y, 0.01) $ $ M=2 $ $ u(x, y, 0.01) $ $ M=5 $ $ u(x, y, 0.01) $ $ M=2 $ -
Figure 3.
Graphical representation of ns of
$ u(x, y, 0.0001) $ $ u(x, y, 0.0001) $ $ u(x, y, 0.0001) $ $ M=2 $ $ u(x, y, 0.0001) $ $ M=5 $ $ u(x, y, 0.0001) $ $ M=2 $ -
Figure 4.
Graphical representation of ns of
$ v(x, y, 0.01) $ $ v(x, y, 0.01) $ $ v(x, y, 0.01) $ $ M=2 $ $ v(x, y, 0.01) $ $ M=5 $ $ v(x, y, 0.01) $ $ M=2 $ -
Figure 5.
Graphical representation of ns of
$ v(x, y, 0.001) $ $ v(x, y, 0.001) $ $ v(x, y, 0.001) $ $ M=2 $ $ v(x, y, 0.001) $ $ M=5 $ $ v(x, y, 0.001) $ $ M=2 $ -
Figure 6.
Graphical representation of ns of
$ v(x, y, 0.0001) $ $ v(x, y, 0.0001) $ $ v(x, y, 0.0001) $ $ M=2 $ $ v(x, y, 0.0001) $ $ M=5 $ $ v(x, y, 0.0001) $ $ M=2 $ -
Figure 7.
Graphical representation of es
$ u(x, t) $ $ k=1 $ $ M=10, 6 $ -
Figure 8.
Graphical representation of es
$ u(x, t) $ $ k=2 $ $ M=5, 3 $ -
Figure 9.
Graphical representation of es
$ v(x, t) $ $ k=1 $ $ M=10, 6 $ -
Figure 1.
Graphical representation of es
$ v(x, t) $ $ k=2 $ $ M=5, 3 $