A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation

Figure 1

Plot comparing the modified equations obtained for explicit (18) (−−−) and implicit (20) (solid line) approximations to the derivative 𝜕𝑢/𝜕𝑥 after substituting the single solitary wave solution to the RLW equation (8) with (18) and (20) taking 𝑣=0.1 and 𝑥₀=0.