N. A. AL-ZAID ET AL. 163

(a) (b)

Figure 4. (a) The exact solution for t = 0.5 and −10 ≤ x ≤ 10; (b) Numerical solution with new modification for t = 0.5 and −10

≤ x ≤ 10.

ADM to solve the RLW equation. The decomposition

series solutions are converge very rapidly in real physical

problems. The numerical results we obtained justify the

advantage of this methodology, even in the few terms

approximation is accurate. The method is tested on the

problem of single solitary motion and high accuracy was

achieved with the L2 and L∞ error norms. The new

Laplace ADM presented here is for the RLW equation,

but it can be implemented to a large number of physically

important nonlinear wave problems.

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