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Full-Text Articles in Applied Mathematics
Modified Gaussian Radial Basis Function Method For The Burgers Systems, Hossein Aminikhah, Mostafa Sadeghi
Modified Gaussian Radial Basis Function Method For The Burgers Systems, Hossein Aminikhah, Mostafa Sadeghi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the systems of variable-coefficient coupled Burgers equation are solved by a free mesh method. The method is based on the collocation points with the modified Gaussian (MGA) radial basis function (RBF). Dependent parameters and independent parameters and their effect on the stability are shown. The accuracy and efficiency of the method has been checked by two examples. The results of numerical experiments are compared with analytical solutions by calculating errors infinity-norm.
Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose
Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose
Rose-Hulman Undergraduate Mathematics Journal
The focus of this research was to develop numerical algorithms to approximate solutions of Poisson's equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson's equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested with an …