In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...

In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...

During present investigation, a direct algebraic method based on complex solutions of nonlinear partial differential equations is developed and tested in the case of generalised Burgers–Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction–diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even i...

The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the ...

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...

In this paper application of a simulation algorithm for dynamic and nonlinear analysis of a specific liquid propellant engine is presented. The mathematical model of the engine includes a set of nonlinear algebraic equations which is coupled with a set of time varying differential equations. In contrast to the existing liquid propellant simulation algorithms, the presented work does not depend ...

The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some ...

A shooting method for two{point{boundary value problems for fully implicit index{ 1 and {2 diierential{algebraic equations is presented. A combination of the shooting equations with a method of the calculation of consistent initial values leads to a system of nonlinear algebraic equations with nonsingular Jacobian. Examples are given.