A fifth order accurate geometric mesh finite difference method for general nonlinear two point boundary value problems

作者：Jha Navnit^*

来源：Applied Mathematics and Computation, 2013, 219(16): 8425-8434.

DOI：10.1016/j.amc.2013.02.069

• Boundary value problems
• Geometric mesh
• Finite difference method
• Convection-diffusion equation
• Newton's method
• Maximum absolute errors

Second order boundary value problems are treated using fifth order accurate geometric mesh finite difference approximations. The method uses evaluation at two off steps, three neighbouring knots and it reduces to simple five terms recurrence relations. The formal convergence analysis and error estimate reveals that the truncation errors of the new discretizations are fifth order accurate. Some physical problems are solved to demonstrate efficiency and reliability of the proposed numerical method. The root mean square errors for different values of mesh ratio parameter have been given in tables to support the utility of the method.

• 出版日期2013-4-15