كاربرد توابع پايه اي شعاعي در حل معادلات برگر وابسته به زمان

‎In this report, we discuss a meshless method for the computation of a numerical solution of unsteady coupled Burgers’-type equations which are‎, ‎in the most general case‎, ‎nonlinear partial differential equations‎. ‎Our approach is based on the interpolation of the solution by radial basis functions (RBFs) and is independent of the geometry of the domain‎. ‎The existence and unicity of such of an interpolant will be established by the mean of linear algebra arguments‎. ‎This spatial discretization transforms the initial problem into a systemofordinarydifferentialequations(ODEs).We give a simple formulation of implicit Runge–Kutta (IRK) schemes that can be used to numerically solve this system of ODEs‎. ‎The main difficulty in the implementation of an IRK method lies in the fact that it leads to a potentially large linear or nonlinear system that has to be solved at each time step‎. ‎A matrix-GMRES approach‎, ‎coupled with a Newton based linearization technique in the nonlinear case,will be used to numerically solve these systems.Some numerical examples will be provided to illustrate the performance of our approach‎.

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رياضي كاربردي - آناليز عددي

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