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A Restrictive Padé approximation for the solution of RLW equation
International Journal of Advances in Applied Mathematics and Mechanics • 2017
Publication Information
Authors
Hassan N.A Ismailab; Khalid M. Elnaggara: Ayman F. Hassana;
Keywords
Partial differential equation (PDE) Regularized long wave (RLW) Restrictive Padé approximation
Journal
International Journal of Advances in Applied Mathematics and Mechanics
Publisher
Not Available
Volume
5
Issue
1
Pages
7-14
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
Solving RLW equation numerically has many difficulties for accuracy. Restrictive Padé (RP) approximation is used.
The numerical solution of RLW equation by RP scheme leads to accurate and efficient results. The stability analysis is
discussed. Numerical results are presented.After solving Examples (1) (section 6.1) and (2) (section 6.2), Table 1 and Table 2 shows comparison between the
absolute error of the considered Restrictive Padé (RP) approximation and highly accurateModified Laplace Adomian
Decomposition method (ADM) which used to solve Example (1) (section 6.1) [27] and variational iteration method which used to solve Example (2) (section 6.2) [28], Also as shown in Example (3) (section 6.3), the change in invariants
is less than 10¡3 and the comparison in Table 4 shows that the norms of error result from present RP method are less
than that we get from Fully implicit method [29]. The results prove that the present method is more accurate than the
previously used methods, i.e. the global error for RP method is less by at least 10¡3 than the previous method.
The numerical solution of RLW equation by RP scheme leads to accurate and efficient results. The stability analysis is
discussed. Numerical results are presented.After solving Examples (1) (section 6.1) and (2) (section 6.2), Table 1 and Table 2 shows comparison between the
absolute error of the considered Restrictive Padé (RP) approximation and highly accurateModified Laplace Adomian
Decomposition method (ADM) which used to solve Example (1) (section 6.1) [27] and variational iteration method which used to solve Example (2) (section 6.2) [28], Also as shown in Example (3) (section 6.3), the change in invariants
is less than 10¡3 and the comparison in Table 4 shows that the norms of error result from present RP method are less
than that we get from Fully implicit method [29]. The results prove that the present method is more accurate than the
previously used methods, i.e. the global error for RP method is less by at least 10¡3 than the previous method.