[PDF] Top 20 Homotopy Analysis Method for Solving Initial Value Problems of Second Order with Discontinuities

... fruitful method (Homotopy Analysis Method (HAM)) for solving linear and nonlinear (ordinary differential, partial differential, integral, ...this method yields a rapid ... See full document

... in solving linear problems however, the Laplace is totally incapable of handling nonlinear equations because of the difficulties that are caused by the nonlinear ... See full document

... kernel method for computing singular second-order initial/boundary value problems ...This method could deal with much more general IBVPs than the ones could do, which are ... See full document

... Euler method will be used as the predictor in this algorithm. This method will act as the initial starting point before the corrector formulae take place to compute the approximation values for y n  ... See full document

... transform method to solve partial differential equations, for finding suitable accurate solutions in a wider ...the problems without resorting to the frequency ...the homotopy perturbation ... See full document

... nonlinear initial value prob- lems (IVPs) is a goal for mathematicians, engineers, and scientists, and it plays an important role in real world ap- ...and second order nonlin- ear IVPs were ... See full document

... new method is applied to non-linear oscillators with discontinuities by He's [15], bifurcation of non-linear problems, periodic solution and bifurcations of delay-dierential equations, limit cycle ... See full document

... boundary value problems generally arise in modelling induction motors with two rotor ...a second rotor circuit representing deep bars, a starting cage, or rotor distributed ... See full document

... perturbed second-order boundary value problem occur very frequently in fluid motion, chemical reactor theory, elasticity, diffusion in polymer, reaction-diffusion equation, control of chaotic system, ... See full document

... [14] Homotopy perturbation method applied to solve variational problems with fixed ...variational problems with moving boundaries problems can be obtained by Homotopy per- ... See full document

... of initial value problems in the second order or- dinary differential equations (ODEs) have been attracted the attention of many mathematicians and ...decomposition method [1-4] ... See full document

... for solving Equa- tion (1) directly without having to reduce to system of first order differential ...solve second order initial value problems which are the mathematical ... See full document

... The second problem considered in this article is the third-order nonlinear Falkner- Skan ...layer problems arise in the study of the flow of electrically con- ducting fluids such as liquid ... See full document

... the homotopy analysis method (HAM), we propose an analytical approach for solving the follow- ing type of nonlinear boundary value problems in finite ...any order of ... See full document

... efficient direct collocation method for the integration of general second order initial value problem.” Journal of Institute of Mathematics and Computer Science, 21, 227-327. [14] ... See full document

... Throughout this paper, an technique for obtaining a numerical solution for second order initial value problems of Bratu-type, is optimal homotopy asymptotic method (OHAM). ... See full document

... [17] Ert ü rkV. S., MomaniS., and OdibatZ., “Application of generalized differential transform method to multi-order fractional differential equations,” Communications in Nonlinear Science and Numerical ... See full document

... The series of equation (15) is convergent for most of the cases, but the rate of the convergence depends on the nonlinear operator  (  ). He (1999) has suggested that: - The second derivative of  (  ) with ... See full document

... a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = ...constant order are reaffirmed in our new ... See full document

... 2009 Solving Singular Second Order Three-Point Boundary Value Problems Using Reproducing Kernel Hilbert Space Method.. 2012 A Numerical Solution to Nonlinear Second Order Three-Point Bou[r] ... See full document