scholarly journals On fundamental solutions of higher‐order space‐fractional Dirac equations

2021 ◽  
Author(s):  
Nelson Faustino
Keyword(s):  
Fundamental Solutions ◽  
Higher Order ◽  
Dirac Equations

REGULARIZATION TECHNIQUES FOR THE METHOD OF FUNDAMENTAL SOLUTIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341004 ◽  
Author(s):  
CSABA GÁSPÁR
Keyword(s):  
Fundamental Solution ◽  
Solution Process ◽  
Partial Differential Operator ◽  
Fundamental Solutions ◽  
Higher Order ◽  
Method Of Fundamental Solutions ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Approximation Theorems ◽  
Regularization Techniques

A special regularization method based on higher-order partial differential equations is presented. Instead of using the fundamental solution of the original partial differential operator with source points located outside of the domain, the original second-order partial differential equation is approximated by a higher-order one, the fundamental solution of which is continuous at the origin. This allows the use of the method of fundamental solutions (MFS) for the approximate problem. Due to the continuity of the modified operator, the source points and the boundary collocation points are allowed to coincide, which makes the solution process simpler. This regularization technique is generalized to various problems and combined with the extremely efficient quadtree-based multigrid methods. Approximation theorems and numerical experiences are also presented.

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