Uniqueness Of Numerical Solution Research Articles

A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term

We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simulations verify that the method is accurate and efficient.

Crank–Nicolson finite difference scheme for the Rosenau–Burgers equation

In this paper, a Crank–Nicolson finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau–Burgers equation is proposed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is convergent in the order of o ( τ 2 + h 2 ) and stable. Numerical simulations show that the method is efficient.

Finite Difference Approximate Solutions for

Existence and uniqueness of numerical solutions are shown for the KdVlike Rosenau equation describing the dynamics of dense discrete systems. A priori bound and the error estimates as well as conservation of energy of the finite difference approximate solutions are discussed with numerical examples.

An almost monotone approximation for a nonlinear two‐point boundary value problem

Almost monotone approximation is proposed for nonlinear two‐points problem. A general framework is given for studying the existence and uniqueness of numerical solutions. A discrete approximation with high accuracy is constructed. Nonlinear Jacobi iteration and Gauss–Seidel iteration are introduced to save work. The continuous approximation is also considered. The numerical results show the advantages of such an approach.