Minimum principle for quadratic spline collocation discretization of a convection-diffusion problem
Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations.
Monotome iterations for spectral approximation of nonlinear layer problem.
Monotone Methods for Periodic solutions of Second Order Scalar Functional Differential Equations.
Monotonicity and Boundedness in Implicit Runge-Kutta Methods.
Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...
Multi-Step Methods are Essentially One-Step Methods.
Multistep methods for ordinary differential equations with parameters
-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Natural Runge-Kutta and Projection Methods.
Necessary and sufficient conditions for the convergence of approximate Picard's iterates for nonlinear boundary value problems
Necessary conditions for the convergence of the generalized periodic overimplicit multistep method
This paper is the continuation of the paper "Generalized periodic overimplicit multistep methods" of the same author and it deals with the necessary and, in some special cases, with the necessary and sufficient conditions for the convergence of general periodic overimplicit multistep methods.
Neurons: a numerical approach.
New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method.
New method for computation of discrete spectrum of radical Schrödinger operator
A new method for computation of eigenvalues of the radial Schrödinger operator is presented. The potential is assumed to behave as if and as if . The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function . It is shown that the eigenvalues are the discontinuity points of the function . Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...
New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke*
We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. A new resolution strategy was recently introduced ? that combines...
New Rosenbrock methods of order 3 for PDAEs of index 2
Newton's Method with Mesh Refinements for Numerical Solution of Nonlinear Two-Point Boundary Value Problems.
Nichtäquidistante Diskretisierungen von Randwertaufgaben.