A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The st...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

The method of exact linearization nonlinear ordinary differential equations (ODE) of order n suggested by one of the authors is demonstrated in [1, 2]. This method is based on the factorization of nonlinear ODE through the first order nonlinear differential the operators, and is also based on using both point and nonpoint, local and nonlocal transformations. Exact linearization of autonomous th...

in this paper, we introduce the new class of implicit l-stable generalized hybrid methods forthe numerical solution of first order initial value problems. we generalize the hybrid methodswith utilize ynv directly in the right hand side of classical hybrid methods. the numericalexperimentation showed that our method is considerably more efficient compared to wellknown methods used for the numer...

This paper is devoted to study the electrochemical behavior of Pt catalyst in a polymer electrolyte fuel cell at various operating conditions and different electric potential difference (also known as voltage) cycling applied accelerated stress tests. The degradation platinum considered with respect dissolution oxide coverage described by one-dimensional model. In model, rate increases temperat...

Developing new and efficient numerical integration techniques is of great importance in applied mathematics computer science. Among the variety available methods, multistep ODE solvers are broadly used simulation software. Recently, semi-implicit proved to be an compromise between implicit explicit solvers, multiple high-performance methods were proposed. However, computational efficiency any s...

In this paper, algorithms for solving of two inverse onedimensional heat transfer problems are considered. They are: the coe cient inverse problem and the determination of phase interface location in a melting problem. These inverse problems are reduced to parameters estimation of ordinary di erential equations (ODE) using a nite element method. The algorithm based on the sensitivity analysis i...