Analysis of higher order difference method for a pseudo-parabolic equation with delay

Solvability of a Higher-Order Nonlinear Neutral Delay Difference Equation

The existence of bounded nonoscillatory solutions of a higher-order nonlinear neutral delay difference equationΔ akn · · ·Δ a2nΔ a1nΔ xn bnxn−d f n, xn−r1n , xn−r2n , . . . , xn−rsn 0, n ≥ n0, where n0 ≥ 0, d > 0, k > 0, and s > 0 are integers, {ain}n≥n0 i 1, 2, . . . , k and {bn}n≥n0 are real sequences, ⋃s j 1{rjn}n≥n0 ⊆ Z, and f : {n : n ≥ n0} × R → R is a mapping, is studied. Some sufficient...

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

On a Higher-Order Nonlinear Difference Equation

and Applied Analysis 3 After k steps we obtain the following formula xn A ⎛ ⎝ A x r/p n−k ⎛ ⎝ A x r/p2 n−k x r/p n−k−1 ⎛ ⎝ A x r/p3 n−k x r/p2 n−k−1x r/p n−k−2

On a Higher-Order Difference Equation

Higher-Order Difference and Higher-Order Splitting Methods for 2D Parabolic Problems with Mixed Derivatives

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...