scholarly journals Numerical algorithm for solving second order nonlinear fuzzy initial value problems

2020 ◽  
Vol 10 (6) ◽  
pp. 6497
Author(s):  
A. F. Jameel ◽  
N. R. Anakira ◽  
A. H. Shather ◽  
Azizan Saaban ◽  
A. K. Alomari
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Initial Value Problems ◽  
Second Order ◽  
Computational Technique ◽  
Solution Properties ◽  
Initial Value ◽  
First Order ◽  
Fuzzy Solution ◽  
Fifth Order

The purpose of this analysis would be to provide a computational technique for the numerical solution of second-order nonlinear fuzzy initial value (FIVPs). The idea is based on the reformulation of the fifth order Runge Kutta with six stages (RK56) from crisp domain to the fuzzy domain by using the definitions and properties of fuzzy set theory to be suitable to solve second order nonlinear FIVP numerically. It is shown that the second order nonlinear FIVP can be solved by RK56 by reducing the original nonlinear equation intoa system of couple first order nonlinear FIVP. The findings indicate that the technique is very efficient and simple to implement and satisfy the Fuzzy solution properties. The method’s potential is demonstrated by solving nonlinear second-order FIVP.

scholarly journals Direct solution of uncertain bratu initial value problem

2019 ◽  
Vol 9 (6) ◽  
pp. 5075
Author(s):  
N. R. Anakira ◽  
A. H. Shather ◽  
A. F. Jameel ◽  
A. K. Alomari ◽  
A. Saaban
Keyword(s):  
Approximate Solution ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Approximate Analytical Solution ◽  
Order System ◽  
Direct Solution ◽  
Initial Value ◽  
First Order ◽  
Bratu Equation ◽  
Variation Iteration Method

<span>In this paper, an approximate analytical solution for solving the fuzzy Bratu equation based on variation iteration method (VIM) is analyzed and modified without needed of any discretization by taking the benefits of fuzzy set theory. VIM is applied directly, without being reduced to a first order system, to obtain an approximate solution of the uncertain Bratu equation. An example in this regard have been solved to show the capacity and convenience of VIM.</span>

scholarly journals Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Nemat Dalir
Keyword(s):  
Fluid Mechanics ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Differential Operators ◽  
Second Order ◽  
Nonlinear Pdes ◽  
Initial Value ◽  
Exact Analytical Solutions ◽  
First Order

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

scholarly journals A 4-Point Block Method for Solving Higher Order Ordinary Differential Equations Directly

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Nazreen Waeleh ◽  
Zanariah Abdul Majid
Keyword(s):  
Initial Value Problems ◽  
Adaptive Strategy ◽  
Variable Step Size ◽  
Block Method ◽  
Initial Value ◽  
Step Size ◽  
First Order ◽  
Variable Step ◽  
Improved Performance ◽  
Fifth Order

An alternative block method for solving fifth-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. The derived method is designed to compute four solutions simultaneously without reducing the problem to a system of first-order IVPs. To validate the proposed method, the consistency and zero stability are also discussed. The improved performance of the developed method is demonstrated by comparing it with the existing methods and the results showed that the 4-point block method is suitable for solving fifth-order IVPs.

The Formation of Implicit Second Order Backward Difference Adam’s Formulae for Solving Stiff Systems of First Order Initial Value Problems of Ordinary Differential Equations

2020 ◽  
pp. 21-29
Author(s):  
Sabo J. ◽  
Kyagya T. Y. ◽  
Ayinde A. M.
Keyword(s):  
Initial Value Problems ◽  
Absolute Stability ◽  
Multistep Method ◽  
Second Order ◽  
Stiff Systems ◽  
Initial Value ◽  
First Order ◽  
Systems Of Odes ◽  
Linear Odes ◽  
Region Of Absolute Stability

The formation of implicit second order backward difference Adam’s formulae for solving stiff systems of ODEs was study in this paper. We used interpolation and collocation in deriving backward differentiae Adam’s formulae. The basic properties of our method was analyzed, and it was found to be consistent, zero-stability and convergent, we further plotted the region of absolute stability and it was shown to be A-stable. Numerical evidences shows that the multistep method develop is very effective method for in handling linear ODEs either initial value problems or boundary value problems.

Nonlinear initial value problems with a singular perturbation of hyperbolic type

1981 ◽  
Vol 89 (3-4) ◽  
pp. 333-345 ◽  
Author(s):  
R. Geel
Keyword(s):  
Initial Value Problems ◽  
A Priori ◽  
Second Order ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Nonlinear Operators ◽  
First Order ◽  
Order Part ◽  
The Difference ◽  
Small Factor

SynopsisThis paper deals with initial value problems in ℝ2 which are governed by a hyperbolic differential equation consisting of a nonlinear first order part and a linear second order part. The second order part of the differential operator contains a small factor ε and can therefore be considered as a perturbation of the nonlinear first order part of the operator.The existence of a solution u together with pointwise a priori estimates for this solution are established by applying a fixed point theorem for nonlinear operators in a Banach space.It is shown that the difference between the solution u and the solution w of the unperturbed nonlinear initial value problem (which follows from the original problem by putting ε = 0) is of order ε, uniformly in compact subsets of ℝ2 where w is sufficiently smooth.

scholarly journals Quasilinearization for the Boundary Value Problem of Second-Order Singular Differential System

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Peiguang Wang ◽  
Tiantian Kong
Keyword(s):  
Boundary Value Problem ◽  
Initial Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Quasilinearization Method ◽  
Initial Value ◽  
First Order ◽  
Monotone Iterative ◽  
Singular Integrodifferential Equations ◽  
The Given

We study the boundary value problems of second-order singular differential equations. At first, we reduce the BVPs to initial value problems of first-order singular integrodifferential equations and then we employ the quasilinearization method in studying the IVPs and obtain two monotone iterative sequences, which converge uniformly and quadratically to the unique solution of the IVPs. Finally, we get the similar result for the given BVPs.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

Categoricity and the sets

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Set Theory ◽  
Second Order ◽  
Order Logic ◽  
First Order ◽  
The Status ◽  
Second Order Logic ◽  
Philosophy Of Set Theory ◽  
Order Set

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.

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