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, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

we study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem, We establish existence results for solutions to the discretized boundary value problems subject to nonlinear bou...

Necessary and sufficient conditions for the existence of finite time singularities for the general solution of systems of ordinary differential equations are given. The systems of ordinary differential equations under consideration form a large subset of the set of all autonomous, nonlinear polynomial ordinary differential equation. The conditions for finite time blowup involve a reality condit...

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...

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...

this paper presents the jeffery hamel flow of a non-newtonian fluid namely casson fluid. suitable similarity transform is applied to reduce governing nonlinear partial differential equations to a much simpler ordinary differential equation. variation of parameters method (vpm) is then employed to solve resulting equation. same problem is solved numerical by using runge-kutta order 4 method. a c...

For the two-dimensional nonlinear system \[ u' = a(t) |v|^{1/\alpha} \operatorname{sgn}v, \quad v' - b(t) |u|^{\alpha} \operatorname{sgn}u \] with $\alpha \gt 0$, $a,b \in C[t_{0},\infty)$, $a(t) \geq 0$ ($t t_{0}$), new oscillation criteria and nonoscillation are given in both cases $\int_{t_{0}}^{\infty} a(s) \, ds \infty$ \lt \infty$. One of main results is an analogue Hartman–Wintner theore...