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 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 An Optimized 5-Point Block Formula for Direct Numerical Solution of First Order Stiff Initial Value Problems

2020 ◽  
Vol 3 (2) ◽  
pp. 158-167
Author(s):  
VO Atabo ◽  
PO Olatunji
Keyword(s):  
Approximate Solution ◽  
Test Performance ◽  
Initial Value Problems ◽  
Power Series Expansion ◽  
Initial Value ◽  
First Order ◽  
Research Article ◽  
Error Constant ◽  
Direct Numerical Solution ◽  
Collocation Approach

In this research article, we focus on the formulation of a 5-point block formula for solving first order ordinary differential equations (ODEs). The method is formulated via interpolation and collocation approach using power series expansion as the approximate solution. It has been established that the derived method is of order six. Basic properties such zero and absolute stabilities, convergence, order and error constant have also been investigated. The accuracy of the method was verified on some selected stiff IVPs, compared with some existing methods (DIBBDF, SDIBBDF, BBDF(4), BBDF(5) and odes15s) and test performance showed that the new method is viable.

scholarly journals Direct integrator of block type methods with additional derivative for general third order initial value problems

2020 ◽  
Vol 12 (10) ◽  
pp. 168781402096618
Author(s):  
Mohammed Yousif Turki ◽  
Fudziah Ismail ◽  
Norazak Senu ◽  
Zarina Bibi Ibrahim
Keyword(s):  
Initial Value Problems ◽  
Numerical Solutions ◽  
Numerical Results ◽  
Order System ◽  
Block Type ◽  
Initial Value ◽  
Third Order ◽  
First Order ◽  
Block Methods ◽  
Hermite Interpolating Polynomial

This paper presents the construction of the two-point and three-point block methods with additional derivatives for directly solving [Formula: see text]. The proposed block methods are formulated using Hermite Interpolating Polynomial and approximate the solution of the problem at two or three-point concurrently. The block methods obtain the numerical solutions directly without reducing the equation into the first order system of initial value problems (IVPs). The order and zero-stability of the proposed methods are also investigated. Numerical results are presented and comparisons with other existing block methods are made. The performance shows that the proposed methods are very efficient in solving the general third order IVPs.

scholarly journals An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
S. J. Kayode
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Numerical Method ◽  
Fourth Order ◽  
Optimal Order ◽  
Direct Solution ◽  
Order Of Accuracy ◽  
First Order ◽  
Stable Numerical Method

The purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order . The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order .

scholarly journals A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations

2020 ◽  
Vol 12 (1) ◽  
pp. 72-82
Author(s):  
Solomon Gebregiorgis ◽  
Hailu Muleta
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Multistep Method ◽  
Stiff Differential Equations ◽  
Block Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order

In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method.  Keywords: Power series, Collocation, Interpolation, Block method, Stiff.

scholarly journals APPROXIMATE SOLUTION OF A NONLINEAR INTEGRO-DIFFERENTIAL EQUATION BY THE NEWTON-KANTOROVICH METHOD

2020 ◽  
pp. 609-614
Author(s):  
I.A. Usenov ◽  
Yu.V. Kostyreva ◽  
S. Almambet kyzy
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Approximate Solution ◽  
Initial Value Problem ◽  
Nonlinear Integral Equation ◽  
Initial Problem ◽  
Initial Value ◽  
Kantorovich Method ◽  
Integro Differential Equation ◽  
First Order

In this paper, we propose a method for studying the initial value problem for a first-order nonlinear integro-differential equation. The initial problem is reduced by substitution to a nonlinear integral equation with the Urson operator. To construct a solution to a nonlinear integral equation, the Newton-Kantorovich method is used.

scholarly journals On solving fuzzy delay differential equation using bezier curves

2020 ◽  
Vol 10 (6) ◽  
pp. 6521
Author(s):  
Ali F. Jameel ◽  
Sardar G. Amen ◽  
Azizan Saaban ◽  
Noraziah H. Man
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Delay Differential Equations ◽  
Bezier Curves ◽  
Bézier Curves ◽  
First Order ◽  
Delay Differential

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.

scholarly journals Integer Interval Value of Milne’s Predictor and Milne’s Corrector Method for First Order ODE

2018 ◽  
Vol 7 (4.10) ◽  
pp. 690
Author(s):  
A. Arul Dass ◽  
G. Veeramalai
Keyword(s):  
Approximate Solution ◽  
Interval Analysis ◽  
Analysis Method ◽  
Life Situation ◽  
Initial Value ◽  
Numerical Illustration ◽  
Interval Method ◽  
First Order ◽  
Interval Analysis Method ◽  
Interval Value

In this paper A new approaches to solve the approximate   solution of   the initial value problem for the first order ordinarydifferential equations and the solution can be used to compute  y numerically specified the value of     near to in the interval analysis method and also used Milne’s predictor and corrector  for interval. In interval method gives a more accurate theapproximate solution of life situation and numerical illustration are given 

A General Approximate Solution for Stretching Problems in Viscous Fluid

2015 ◽  
Vol 70 (9) ◽  
pp. 781-786
Author(s):  
Saleem Asghar ◽  
Mudassar Jalil ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Boundary Value Problem ◽  
Analytic Solution ◽  
Boundary Value ◽  
Skin Friction Coefficient ◽  
Order System ◽  
First Order ◽  
Exponential Stretching ◽  
Special Cases

AbstractIn this study, we propose a boundary value problem that contains two arbitrary parameters in the differential equation and show that the results of a number of existing stretching problems (linear, power law, and exponential stretching) are the special cases of the proposed boundary value problem. A two-term analytic asymptotic solution of this problem is developed by introducing a small parameter in the differential equation. Interest lies in the finding of rare exact analytical solutions for the zeroth and first order systems. Surprisingly, only a two-term closed form of analytical solution shows an excellent match with the existing literature. The solution for second-order system is found numerically to improve the accuracy of the approximate solution. The generalised analytic solution is tested over a number of stretching problems for the velocity field and skin friction coefficient showing an excellent match. In conclusion, various stretching problems discussed in literature are special cases of this study.

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