A spline collocation method for integrating a class of chemical reactor equations

Elhajaji, Abdelmajid; Barje, Nadia; Serghini, Abdelhafid; Hilal, Khalid; Mermri, El Bekkaye

doi:10.22075/ijnaa.2017.1653.1436

A spline collocation method for integrating a class of chemical reactor equations

Document Type : Research Paper

Authors

Abdelmajid Elhajaji ¹

Nadia Barje ²

Abdelhafid Serghini ³

Khalid Hilal ²

El Bekkaye Mermri ⁴

¹ ENCG El Jadida

² LMC Laboratory, FST, University of Sultan Moulay Slimane, Beni-Mellal, Morocco

³ MATSI Laboratory, ESTO, University Mohammed Premier, Oujda, Morocco

⁴ Department of Mathematics and Computer Science, FS, University Mohammed Premier, Oujda, Morocco

10.22075/ijnaa.2017.1653.1436

Abstract

. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the proposed spline collocation method for the spatial discretization. The design of the collocation method is interpreted as one order error convergent. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behavior of the rates of convergence.

Keywords

Partial differential equations

Distributed parameter systems

Plus flow reactors

Perturbed systems

Spline collocation method