A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions
ملخص البحث
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations
subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral
approximation is investigated for the discretization of the spatial variable of such equations. It possesses
spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is
established for treating the non-local conservation conditions, and then the problem with its initial and
non-local boundary conditions are reduced to a system of second-order ordinary differential equations in
temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical
examples with comparisons are given. The computational results demonstrate that the proposed
algorithm is more accurate than finite difference method, method of lines and spline collocation approach.
الكلمات المفتاحيه
non-local boundary conditions • integral conservation condition • collocation method • shifted Jacobi-Gauss- Lobatto quadrature • system of differential equations