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.