Trefftz Methods for Time Dependent Partial Differential Equations

摘要: In this paper we present a mesh-free ap- proach to numerically solving class of second order time dependent partial differential equations which in- clude parabolic, hyperbolic and parabolic- types. For numerical purposes, variety transformations is used convert these stan- dard reaction-diffusion wave equation forms. To solve initial boundary value problems for equa- tions, the dependence removed by either Laplace or Laguerre transform differencing, converts problem into one se- quence inhomogeneous modified Helmholtz equations. These are then solved combination method particular solutions Trefftz methods. do this, techniques proposed com- puting solution mod- ified equation. Here, focus on Dual Reciprocity Method where source term approxi- mated radial basis functions, polynomial trigono- metric functions. Analytic pre- sented each approximations. The resulting homogenous obtained after approximate solu- tion subtracted off. Two types bases con- sidered, F-Trefftz based fundamental equation, T-Trefftz separation variables solutions. Var- ious satisfying conditions considered, discussion given mitigating ill-conditioning linear systems. Finally, some results presented il- lustrating accuracy efficacy methodology.