scholarly journals The relationship between the solutions according to the noniterative method and the generalized differentiability of the fuzzy boundary value problem

2018 ◽  
Vol 06 (04) ◽  
pp. 781-787 ◽  
Author(s):  
Hülya Gültekin Çitil
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Generalized Differentiability ◽  
Fuzzy Boundary ◽  
The Relationship

scholarly journals Formal Consistency Versus Actual Convergence Rates of Difference Schemes for Fractional-Derivative Boundary Value Problems

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
José Luis Gracia ◽  
Martin Stynes
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Convergence Rates ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Polynomial Solution ◽  
Difference Schemes ◽  
Smooth Functions ◽  
Numerical Performance ◽  
The Relationship

AbstractFinite difference methods for approximating fractional derivatives are often analyzed by determining their order of consistency when applied to smooth functions, but the relationship between this measure and their actual numerical performance is unclear. Thus in this paper several wellknown difference schemes are tested numerically on simple Riemann-Liouville and Caputo boundary value problems posed on the interval [0, 1] to determine their orders of convergence (in the discrete maximum norm) in two unexceptional cases: (i) when the solution of the boundary-value problem is a polynomial (ii) when the data of the boundary value problem is smooth. In many cases these tests reveal gaps between a method’s theoretical order of consistency and its actual order of convergence. In particular, numerical results show that the popular shifted Gr¨unwald-Letnikov scheme fails to converge for a Riemann-Liouville example with a polynomial solution p(x), and a rigorous proof is given that this scheme (and some other schemes) cannot yield a convergent solution when p(0)≠ 0.

scholarly journals Important Notes for a Fuzzy Boundary Value Problem

2019 ◽  
Vol 4 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Hülya Gültekin Çitil
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Liouville Problem ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Fuzzy Boundary

AbstractIn this paper is studied a fuzzy Sturm-Liouville problem with the eigenvalue parameter in the boundary condition. Important notes are given for the problem. Integral equations are found of the problem.

scholarly journals Solution of generalised type – 2 Fuzzy boundary value problem

2021 ◽  
Vol 60 (2) ◽  
pp. 2725-2739
Author(s):  
S. Tudu ◽  
S.P. Mondal ◽  
A. Ahmadian ◽  
A.K. Mahmood ◽  
S. Salahshour ◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Fuzzy Boundary

scholarly journals Efficient approximate analytical methods for nonlinear fuzzy boundary value problem

2022 ◽  
Vol 12 (2) ◽  
pp. 1916
Author(s):  
Ali Fareed Jameel ◽  
Hafed H Saleh ◽  
Amirah Azmi ◽  
Abedel-Karrem Alomari ◽  
Nidal Ratib Anakira ◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Analytical Methods ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Numerical Comparison ◽  
Fuzzy Boundary Value Problems ◽  
Fuzzy Boundary ◽  
Approximate Analytical Methods

This paper aims to solve the nonlinear two-point fuzzy boundary value problem (TPFBVP) using approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be challenging to evaluate. Therefore, approximate analytical methods may be necessary to consider the solution. Hence, there is a need to formulate new, efficient, more accurate techniques. This is the focus of this study: two approximate analytical methods-homotopy perturbation method (HPM) and the variational iteration method (VIM) is proposed. Fuzzy set theory properties are presented to formulate these methods from crisp domain to fuzzy domain to find approximate solutions of nonlinear TPFBVP. The presented algorithms can express the solution as a convergent series form. A numerical comparison of the mean errors is made between the HPM and VIM. The results show that these methods are reliable and robust. However, the comparison reveals that VIM convergence is quicker and offers a swifter approach over HPM. Hence, VIM is considered a more efficient approach for nonlinear TPFBVPs.

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