Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind sch...Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.展开更多
Framework definitions of earlier informally used notions of effect and phenomenon are proposed, examples of their role in developing mathematics are given. Phenomena of singular cycle and deepening boundary layer in t...Framework definitions of earlier informally used notions of effect and phenomenon are proposed, examples of their role in developing mathematics are given. Phenomena of singular cycle and deepening boundary layer in the theory of singularly perturbed differential equations and ancient popular synergetic process described by system of random difference equations are presented.展开更多
基金supported by the Department of Science & Technology, Government of India under research grant SR/S4/MS:318/06.
文摘Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.
文摘Framework definitions of earlier informally used notions of effect and phenomenon are proposed, examples of their role in developing mathematics are given. Phenomena of singular cycle and deepening boundary layer in the theory of singularly perturbed differential equations and ancient popular synergetic process described by system of random difference equations are presented.
