Collocation method using quintic B-splines finite element have been developed for solving numerically the HirotaSatsuma coupled MKdV equation. Accuracy of the proposed method is shown numerically by calculating conservation laws, 2 L and  L norms on studying of a soliton solution. It is shown that the collocation scheme for solutions of the MKdV equation gives rise to smaller errors and is qui...

Abstract. A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the...

Most mathematical models contain uncertainties that may be originated from various sources such as initial and boundary conditions, geometry representation of the domain and input parameters. When these sources are expressed as random processes or random fields, partial differential equations describing the underlying models become stochastic partial differential equations (SPDEs). Stochastic m...

The paper proposed to use recurrent Fuzzy-Neural Multi-Model (FNMM) identifier for decentralized identification of a distributed parameter anaerobic wastewater treatment digestion bioprocess, carried out in a fixed bed and a recirculation tank. The distributed parameter analytical model of the digestion bioprocess is used as a plant data generator. It is reduced to a lumped system using the ort...

-Gradient elution in nonlinear chromatography is a very powerful tool for the separation of components having a wide range of retentivity. It is not only used for chemical analysis, but also used in preparativeand large-scale chromatography for the separation of many macromolecules, such as proteins. In this work, a general rate model has been presented for the study of gradient elution in nonl...

This paper is devoted to the numerical comparison of methods applied to solve problems with nonlocal boundary conditions. Four numerical methods are compared, namely, finite differences method, Galerkin method, Keller Box scheme and orthogonal spline collocation method. Mathematics Subject Classification: 74S05, 74S20, 74S30, 74H15

In recent years, there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary/partial differential equations. To this end, the spectral stochastic finite element method (SSFEM) is the most popular method due to its fast convergence rate. Recently, the stochastic sparse grid collocation method has emerged as an attractive alternative to ...

In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important ...

Techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau, and least-squares methods, are adopted to solve a non-linear and highly coupled pellet problem. Based on a residual measure and problem matrix condition numbers, the Galerkin and tau methods are favorable solution techniques for the pellet equations. On the other hand, the orthogonal collocation is...