The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of 2-hyperconvex and 2-hyperconcave functions. We develop two sequences under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence is of order 3. Finally, we provide numerical examples to sho...

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct. Keywords—Nonlinear equations, Secant method, Convergence order, Secant-like method.

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.

We present a new numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method, propose fully discrete schemes based on elementary quadrature formulas and show that the perturb...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...