Error analysis of the Chebyshev collocation method for linear second-order partial differential equations

2014 ◽  
Vol 92 (10) ◽  
pp. 2121-2138 ◽  
Author(s):  
Gamze Yuksel ◽  
Osman Rasit Isik ◽  
Mehmet Sezer
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Analysis ◽  
Collocation Method ◽  
Second Order ◽  
Chebyshev Collocation Method ◽  
Partial Differential ◽  
Chebyshev Collocation

scholarly journals Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
B. A. Jacobs ◽  
C. Harley
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Hybrid Methods ◽  
Test Problems ◽  
Spatial Discretization ◽  
Chebyshev Collocation Method ◽  
Partial Differential ◽  
Chebyshev Collocation

A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

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