Higher-order MUSCL scheme for transport equation originating in a neuronal model

We consider a transport equation with mixed boundary conditions (Dirichlet and Neumann) originating in a neuronal model. This equation contains point-wise delay and advanced argument. The objective of this paper is to construct and analyze higher order MUSCL scheme to find a numerical solution. The developed scheme is stable and convergent. The importance of this scheme is that it is valid for large as well as for small values of point-wise delay and advance. Some test examples are included to examine the behavior of the solution and to verify the order of convergence. The effect of point-wise delay and advance arguments on the solution is shown graphically.