APPLICATION OF HOMOTOPY ANALYSIS METHOD (HAM) TO THE NON-LINEAR KDV EQUATIONS
Copyright policy )APPLICATION OF HOMOTOPY ANALYSIS METHOD (HAM) TO THE NON-LINEAR KDV EQUATIONS
In this work, approximate analytic solutions for different types of KdV equations are obtained using the homotopy analysis method (HAM). The convergence control parameter h helps us to adjust the convergence region of the approximate analytic solutions. The solutions are obtained in the form of power series. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. We have compared the approximate analytical results which are determined by HAM, with the exact solutions and shown graphically with their absolute errors. By choosing an appropriate value of the convergence control parameter, we can obtain the solution in few iterations. All the computations have been performed using the software package MATHEMATICA.
homotopy analysis method, Analyticity in context of PDEs, convergence control parameter, Symbolic computation and algebraic computation, Solutions to PDEs in closed form, symbolic computation, KdV equations (Korteweg-de Vries equations), Series solutions to PDEs, KdV equations, approximate series solutions, [MATH]Mathematics [math], Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
homotopy analysis method, Analyticity in context of PDEs, convergence control parameter, Symbolic computation and algebraic computation, Solutions to PDEs in closed form, symbolic computation, KdV equations (Korteweg-de Vries equations), Series solutions to PDEs, KdV equations, approximate series solutions, [MATH]Mathematics [math], Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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