ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD

Mashuri, Mashuri
Zakiyah, Yayah
Reorita, Rina

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications

In this research we discussed about the solution of the KdV equation using Homotopy Perturbation method. The KdV equation that describing water wave equation solved by using the mixing method between Homotopy and Perturbation method. Homotopy was built with embedding parameter p∈[0,1] which undergoes a deformation process from linear problems to nonlinear problems and the assumed solution of the KdV equation is expressed in the form of a power series p up to the third order. The result show that in each order solution we obtained resonance term. for handling the condition, we used Lindsteadt-Poincare method.the wave number k2 and dispersion relation can be obtained in the second order solution as the effect of using Lindsteadt-Poincare method.