An efficient collocation method with convergence rates based on Müntz spaces for solving nonlinear fractional two-point boundary value problems

2020 ◽  
Vol 39 (4) ◽  
Author(s):  
S. Erfani ◽  
S. Javadi ◽  
E. Babolian
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Convergence Rates ◽  
Boundary Value ◽  
Point Boundary ◽  
Müntz Spaces

scholarly journals Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2104
Author(s):  
Kenzu Abdella ◽  
Jeet Trivedi
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Excellent Performance ◽  
Unknown Variable ◽  
First Derivative ◽  
Linear And Nonlinear

In this paper, the Sinc-derivative collocation method is used to solve linear and nonlinear multi-point boundary value problems. This is done by interpolating the first derivative of the unknown variable via Sinc numerical methods and obtaining the desired solution through numerical integration of the interpolation and all higher order derivatives through successive differentiation of the interpolation. Non-homogeneous boundary conditions are reduced to homogeneous using suitable transformations. The efficiency and the accuracy of the method are tested using illustrative examples previously considered by other researchers who used different approaches. The results show the excellent performance of the Sinc-derivative collocation method.

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