3rd International Conference on Pure and Applied Mathematics ICPAM-VAN 2020, Van, Turkey, 3 - 05 September 2020, pp.111
In this study we aim to develop a Maxima  package for analytical solution of linear system of one dimensional transport equations of the form
U_t + A_Ux = B_Uxx + CU + D (1)
where U = (u,v) is the vector of unknowns, A, B and C are 2 × 2 constant matrices and D 2×1 is a constant vector. The package aims to solve the system over a finite interval with Dirichlet and Neumann boundary conditions, as well as Robin conditions with the aid of some numerical methods that may be needed for numerical computation of eigenvalues. The package aims to interactively asks for problem data (the coefficient matrices, initial and boundary conditions) and display both analytical solution and its graph if desired. Initial results for scalar transport equation will be illustrated.
The motivation for the study came from a research work on wound healing model being studied by the authors.
MSC 2010: 35E05, 35E20, 35Q92, 35G35, 68U01
Keywords: Transport equation, analytic solution of partial differential equations, Maxima packages
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