Numerical solution of Boundary value problems
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For solving complex linear and nonlinear differential equations a new perturbation method called the homotopy perturbation method (HPM) was proposed by Ji-Huan He in 1999 which is, in fact, a coupling of the traditional perturbation method and homotopy in topology. In this method, the solution is considered as the summation of an infinite series, which usually converges rapidly to the exact solution. This new method was further developed and improved by He and applied to non-linear oscillators with discontinuities, non-linear wave equations, limit cycle and bifurcations, non-linear boundary va...
For solving complex linear and nonlinear differential equations a new perturbation method called the homotopy perturbation method (HPM) was proposed by Ji-Huan He in 1999 which is, in fact, a coupling of the traditional perturbation method and homotopy in topology. In this method, the solution is considered as the summation of an infinite series, which usually converges rapidly to the exact solution. This new method was further developed and improved by He and applied to non-linear oscillators with discontinuities, non-linear wave equations, limit cycle and bifurcations, non-linear boundary value problems , asymptotology and many other subjects. He's polynomials introduced by Ghorbani et al. which are well-matched with Adomian's polynomials but are informal to calculate. By studying this book , reader will learn about the method and able to solve various problems arising in the field of science ,engineering & technology.
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