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Full-Text Articles in Applied Mathematics
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
Rose-Hulman Undergraduate Mathematics Journal
We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.
Novel Techniques For Solving Goursat Partial Differential Equations In The Linear And Nonlinear Regime, Tahir Naseem
Novel Techniques For Solving Goursat Partial Differential Equations In The Linear And Nonlinear Regime, Tahir Naseem
International Journal of Emerging Multidisciplinaries: Mathematics
The Goursat problem, which is related to hyperbolic partial differential equations, occurs in a variety of branches of physics and engineering. We studied the solution of the Goursat partial differential equation utilizing the reduced differential transform (RDT) and Adomian decomposition (AD) techniques in this inquiry. The problem's analytical solution is found in series form, which converges to exact solutions. The approaches' reliability and efficiency were evaluated using the Goursat problems (linear and non-linear). Additionally, the accuracy of the findings obtained demonstrates the reduced differential approach's superiority over the Adomian decomposition method and other numerical methods previously applied to the Goursat …
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 …