Viscosity solutions of second order partial differential equations with boundary conditions on Riemannian manifolds

2016 ◽  
Vol 146 ◽  
pp. 211-232
Author(s):  
S. Khajehpour ◽  
M.R. Pouryayevali
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Viscosity Solutions ◽  
Riemannian Manifolds ◽  
Second Order ◽  
Partial Differential

A Numerical Method for Solving Second-Order Linear Partial Differential Equations Under Dirichlet, Neumann and Robin Boundary Conditions

2017 ◽  
Vol 14 (02) ◽  
pp. 1750015 ◽  
Author(s):  
Şuayip Yüzbaşı
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Second Order ◽  
Robin Boundary Conditions ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Robin Boundary

The aim of this paper is to give a collocation method to solve second-order partial differential equations with variable coefficients under Dirichlet, Neumann and Robin boundary conditions. By using the Bessel functions of the first kind, the matrix operations and the collocation points, the method is constructed and it transforms the partial differential equation problem into a system of algebraic equations. The unknown coefficients of the assuming solution are determined by solving this system. The algorithm of the proposed method is presented. Also, error estimation technique is introduced and the approximate solutions are improved by means of it. To show the validity and applicability of the presented method, we solve numerical examples and give the comparison of solutions and comparisons of the errors (actual and estimation).

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