1. bookVolume 80 (2021): Edition 3 (December 2021)
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A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

Publié en ligne: 01 Jan 2022
Volume & Edition: Volume 80 (2021) - Edition 3 (December 2021)
Pages: 15 - 34
Reçu: 03 Mar 2020
Détails du magazine
License
Format
Magazine
eISSN
1338-9750
Première parution
12 Nov 2012
Périodicité
3 fois par an
Langues
Anglais
Abstract

In this paper, we develop a new numerical algorithm for solving a time dependent convection-diffusion equation with Dirichlet’s type boundary conditions. The method comprises the horizontal method of lines for time integration and (θ-method, θ ∈ [1/2, 1] (θ = 1 corresponds to the backward Euler method and θ = 1/2 corresponds to the Crank-Nicolson method) to discretize in temporal direction and the quintic spline collocation method. The convergence analysis of proposed method is discussed in detail, and it justified that the approximate solution converges to the exact solution of orders Ot + h3) for the backward Euler method and Ot2 + h3) for the Crank-Nicolson method, where Δt and h are mesh sizes in the time and space directions, respectively. It is also shown that the proposed method is unconditionally stable. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behaviour of the rates of convergence. Results shown by this method are in good agreement with the known exact solutions. The produced results are also more accurate than some available results given in the literature.

Keywords

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