An accurate and cost-efficient numerical approach to analyze the initial and boundary value problems of fractional multi-order

2018 ◽  
Vol 37 (5) ◽  
pp. 6582-6600 ◽  
Author(s):  
K. Sayevand ◽  
J. Tenreiro Machado
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Numerical Approach ◽  
Cost Efficient

scholarly journals Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Oluwaseun Adeyeye ◽  
Zurni Omar
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Numerical Approach ◽  
Squeezing Flow ◽  
Nonlinear Boundary Value Problems ◽  
Block Method ◽  
Nonlinear Boundary Value ◽  
Improved Accuracy

Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A m+1th-step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where m is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at m+1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the m+1th-step block method was displayed in the solution for magnetohydrodynamic squeezing flow in porous medium.

scholarly journals Solution of two point boundary value problems, a numerical approach: parametric difference method

2018 ◽  
Vol 3 (2) ◽  
pp. 649-658 ◽  
Author(s):  
P.K. Pandey
Keyword(s):  
Exact Solution ◽  
Boundary Value Problems ◽  
Difference Method ◽  
Model Problem ◽  
Mixed Boundary ◽  
Numerical Technique ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Numerical Approach ◽  
Point Boundary

AbstractIn this article, we have presented a parametric finite difference method, a numerical technique for the solution of two point boundary value problems in ordinary differential equations with mixed boundary conditions. We have tested proposed method for the numerical solution of a model problem. The numerical results obtained for the model problem with constructed exact solution depends on the choice of parameters. The computed result of a model problem suggests that proposed method is efficient.

scholarly journals The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Esmael Samei ◽  
Ahmad Ahmadi ◽  
Sayyedeh Narges Hajiseyedazizi ◽  
Shashi Kant Mishra ◽  
Bhagwat Ram
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Time Scale ◽  
Boundary Value ◽  
Numerical Approach ◽  
Differential Problem ◽  
Nonlinear Alternative ◽  
Nonnegative Solutions

AbstractThis paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional q-differential equation ${}^{c}\mathcal{D}_{q}^{\sigma }[k](t) = w (t, k(t), {}^{c} \mathcal{D}_{q}^{\zeta }[k](t) )$ D q σ c [ k ] ( t ) = w ( t , k ( t ) , c D q ζ [ k ] ( t ) ) with three-point conditions for $t \in (0,1)$ t ∈ ( 0 , 1 ) on a time scale $\mathbb{T}_{t_{0}}= \{ t : t =t_{0}q^{n}\}\cup \{0\}$ T t 0 = { t : t = t 0 q n } ∪ { 0 } , where $n\in \mathbb{N}$ n ∈ N , $t_{0} \in \mathbb{R}$ t 0 ∈ R , and $0< q<1$ 0 < q < 1 , based on the Leray–Schauder nonlinear alternative and Guo–Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

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