Efficient Algorithms for Solving Partial Differential Equations with Discontinuous Solutions
نویسنده
چکیده
P artial differential equations (PDEs) arise in numerous scientific and engineering applications. Mathematical modeling in various applications often ends up with a set of PDEs. Mathematical techniques can help to understand many crucial properties of the PDEs, such as existence and uniqueness of solutions under suitable initial and/or boundary conditions, and the well-posedness of the problem, which refers to the fact that the change of the solution for later time is controlled by the change of the initial condition or the change of the solution inside the domain is controlled by the change of the boundary data. However, for the vast majority of PDEs from applications, it is not possible to obtain explicit formulas for their solutions. Thus, in scientific and engineering applications, it is necessary to solve the PDEs numerically, that is, using certain algorithms to obtain approximate solutions to the PDEs on a computer.
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