AN ACCURATE LEGENDRE COLLOCATION SCHEME FOR COUPLED HYPERBOLIC EQUATIONS WITH VARIABLE COEFFICIENTS
ملخص البحث
The study of numerical solutions of nonlinear coupled hyperbolic partial differential
equations (PDEs) with variable coefficients subject to initial-boundary conditions
continues to be a major research area with widespread applications in modern
physics and technology. One of the most important advantages of collocation method is
the possibility of dealing with nonlinear partial differential equations (NPDEs) as well
as PDEs with variable coefficients. A numerical solution based on a Legendre collocation
method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients.
This approach, which is based on Legendre polynomials and Gauss-Lobatto
quadrature integration, reduces the solving of nonlinear coupled hyperbolic PDEs with
variable coefficients to a system of nonlinear ordinary differential equations that is far
easier to solve. The obtained results show that the proposed numerical algorithm is
efficient and very accurate.
الكلمات المفتاحيه
Nonlinear coupled hyperbolic partial differential equations; Nonlinear phenomena; Collocation method; Gauss-Lobatto quadrature