The numerical solution of the one-dimensional heat equation by using third degree B-spline functions

2008 ◽  
Vol 38 (4) ◽  
pp. 1197-1201 ◽  
Author(s):  
Hikmet Çağlar ◽  
Mehmet Özer ◽  
Nazan Çağlar
Keyword(s):  
Heat Equation ◽  
Numerical Solution ◽  
Spline Functions ◽  
B Spline ◽  
One Dimensional ◽  
The One

scholarly journals An Approximate Solution of the Space Fractional-Order Heat Equation by the Non-Polynomial Spline Functions

2021 ◽  
pp. 2327-2333
Author(s):  
Nabaa N. Hasan ◽  
Omar H. Salim
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Fractional Derivatives ◽  
Polynomial Spline ◽  
Spline Functions ◽  
Two Dimensional ◽  
Fractional Partial Differential Equation ◽  
Numerical Examples ◽  
One Dimensional ◽  
The One

     The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.

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