Here ordinary differential equations of third and higher order are considered; in particular, a class of equations which can be solved by quadratures is exploited. Indeed, crucial to obtain our result is the property of the Riccati equation, according to which, given one particular solution, then its general solution can be determined explicitly. Thus, what we term the “Riccati” Property is int...

A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resu...

in this paper, we adapt the operational tau method for personal computers and apply it to a system of two nonlinear second order ordinary differential equations which are related to general relativity. the interesting behaviour this problem exhibits in its numerical treatment is discussed. in this problem, we try to use the tau perturbation term to locate the correct solution of this nonlinear ...

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

Abstract In this work, a technique for finding approximate solutions ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is hybrid between Galerkin and collocation methods. Also, can be extended to fractional integro-differential (FIDEs) optimal control problems (FOCPs). spatial approximations with their derivatives are based on shifted ultraspherical pol...