scholarly journals High accuracy cubic spline approximation for two dimensional quasi-linear elliptic boundary value problems

2013 ◽  
Vol 37 (1-2) ◽  
pp. 155-171 ◽  
Author(s):  
R.K. Mohanty ◽  
M.K. Jain ◽  
Deepika Dhall
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Spline Approximation ◽  
Cubic Spline ◽  
High Accuracy ◽  
Elliptic Boundary Value Problems ◽  
Two Dimensional ◽  
Elliptic Boundary Value ◽  
Linear Elliptic Boundary

Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Harendra Singh
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
High Accuracy ◽  
Elliptic Boundary Value Problems ◽  
Strong Nonlinearity ◽  
Elliptic Boundary Value ◽  
Chebyshev Spectral Collocation ◽  
Chebyshev Spectral Method ◽  
Chebyshev Spectral Collocation Method

Abstract This paper deals with a class of Bratu’s type, Troesch’s and nonlocal elliptic boundary value problems. Due to strong nonlinearity and presence of parameter δ, it is very difficult to solve these problems. Here we solve these classes of important equations using the Chebyshev spectral collocation method. We have provided the convergence of the proposed approximate method. The trueness of the method is shown by applying it to some illustrative examples. Results are compared with some known methods to highlight its neglectable error and high accuracy.

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