Solving hyperbolic partial differential equations using a highly accurate multidomain bivariate spectral collocation method

Wave Motion ◽  
2019 ◽  
Vol 88 ◽  
pp. 57-72
Author(s):  
F.M. Samuel ◽  
S.S. Motsa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Hyperbolic Partial Differential Equations ◽  
Spectral Collocation ◽  
Partial Differential

scholarly journals An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. A. Alghamdi ◽  
Eman S. Alaidarous
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Jacobi Polynomials ◽  
Nonlocal Conditions ◽  
Initial Boundary ◽  
Variable Coefficients ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Hyperbolic Pdes

One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs) as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

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