A fourth-order accurate quasi-variable mesh compact finite-difference scheme for two-space dimensional convection-diffusion problems

Advances in Difference Equations

Neelesh Kumar¹  Navnit Jha¹ 

[1] Faculty of Mathematics and Computer Science, South Asian University, Chanakyapuri, India

关键词: convection-diffusion equation;    compact scheme;    finite-difference method;    quasi-variable meshes;    irreducible and monotone matrix;    maximum absolute error;    root-mean squared error;    65N06;    65N12;    35J57;    35J72;   

DOI  :  10.1186/s13662-017-1115-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We discuss a new nine-point fourth-order and five-point second-order accurate finite-difference scheme for the numerical solution of two-space dimensional convection-diffusion problems. The compact operators are defined on a quasi-variable mesh network with the same order and accuracy as obtained by the central difference and averaging operators on uniform meshes. Subsequently, a high-order difference scheme is developed to get the numerical accuracy of order four on quasi-variable meshes as well as on uniform meshes. The error analysis of the fourth-order compact scheme is described in detail by means of matrix analysis. Some examples related with convection-diffusion equations are provided to present performance and robustness of the proposed scheme.

【 授权许可】

CC BY