Error estimates of generalized spectral iterative methods with accurate convergence rates for solving systems of fractional two - point boundary value problems

2020 ◽  
Vol 364 ◽  
pp. 124638 ◽  
Author(s):  
S. Erfani ◽  
E. Babolian ◽  
S. Javadi
Keyword(s):  
Boundary Value Problems ◽  
Iterative Methods ◽  
Error Estimates ◽  
Convergence Rates ◽  
Boundary Value ◽  
Point Boundary

scholarly journals The Error Estimates of the Interpolating Element-Free Galerkin Method for Two-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
J. F. Wang ◽  
S. Y. Hao ◽  
Y. M. Cheng
Keyword(s):  
Boundary Value Problems ◽  
Convergence Rates ◽  
Boundary Value ◽  
Weak Form ◽  
Point Boundary ◽  
Element Free Galerkin Method ◽  
Original Solution ◽  
Element Free Galerkin ◽  
Element Free ◽  
Derivatives Of

The interpolating moving least-squares (IMLS) method is discussed in detail, and a simpler formula of the shape function of the IMLS method is obtained. Then, based on the IMLS method and the Galerkin weak form, an interpolating element-free Galerkin (IEFG) method for two-point boundary value problems is presented. The IEFG method has high computing speed and precision. Then error analysis of the IEFG method for two-point boundary value problems is presented. The convergence rates of the numerical solution and its derivatives of the IEFG method are presented. The theories show that, if the original solution is sufficiently smooth and the order of the basis functions is big enough, the solution of the IEFG method and its derivatives are convergent to the exact solutions in terms of the maximum radius of the domains of influence of nodes. For the purpose of demonstration, two selected numerical examples are given to confirm the theories.

Sign in / Sign up

Export Citation Format

Share Document