scholarly journals Numerical Solution of Second-Order Fuzzy Differential Equation Using Improved Runge-Kutta Nystrom Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Faranak Rabiei ◽  
Fudziah Ismail ◽  
Ali Ahmadian ◽  
Soheil Salahshour
Keyword(s):  
Differential Equation ◽  
Computational Cost ◽  
Second Order ◽  
Fuzzy Differential Equation ◽  
Nyström Method ◽  
Numerical Examples ◽  
Time Consumption ◽  
Nystrom Method ◽  
Fuzzy Function ◽  
Runge Kutta

We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of function evaluations in comparison with the existing Fuzzy Runge-Kutta Nystrom method. Therefore, the new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. FIRKN methods of orders three, four, and five are derived with two, three, and four stages, respectively. The numerical examples are given to illustrate the efficiency of the methods.

scholarly journals A Zero-Dissipative Runge-Kutta-Nyström Method with Minimal Phase-Lag

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Norazak Senu ◽  
Mohamed Suleiman ◽  
Fudziah Ismail ◽  
Mohamed Othman
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Phase Lag ◽  
Nyström Method ◽  
Numerical Comparisons ◽  
Nystrom Method ◽  
Second Order Differential Equations ◽  
Runge Kutta ◽  
Minimal Phase

An explicit Runge-Kutta-Nyström method is developed for solving second-order differential equations of the formq′′=f(t,q)where the solutions are oscillatory. The method has zero-dissipation with minimal phase-lag at a cost of three-function evaluations per step of integration. Numerical comparisons with RKN3HS, RKN3V, RKN4G, and RKN4C methods show the preciseness and effectiveness of the method developed.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

Modeling the scalar wave equation with Nyström methods

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. T151-T158 ◽  
Author(s):  
Jing-Bo Chen
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Second Order ◽  
Scalar Wave ◽  
Nyström Method ◽  
Scalar Wave Equation ◽  
Nystrom Method ◽  
Nyström Methods ◽  
Long Time ◽  
Order Scheme

High-accuracy numerical schemes for modeling of the scalar wave equation based on Nyström methods are developed in this paper. Space is discretized by using the pseudospectral algorithm. For the time discretization, Nyström methods are used. A fourth-order symplectic Nyström method with pseudospectral spatial discretization is presented. This scheme is compared with a commonly used second-order scheme and a fourth-order nonsymplectic Nyström method. For a typical time-step size, the second-order scheme exhibits spatial dispersion errors for long-time simulations, while both fourth-order schemes do not suffer from these errors. Numerical comparisons show that the fourth-order symplectic algorithm is more accurate than the fourth-order nonsymplectic one. The capability of the symplectic Nyström method in approximately preserving the discrete energy for long-time simulations is also demonstrated.

Dynamic Analysis of Soft Tissues Using a State Space Model

2008 ◽  
Author(s):  
Assimina Pelegri ◽  
Baoxiang Shan
Keyword(s):  
Differential Equation ◽  
Dynamic Analysis ◽  
State Space ◽  
Soft Tissues ◽  
Order Differential Equation ◽  
Computational Cost ◽  
Second Order ◽  
P Element ◽  
Fe Model ◽  
Second Order Differential Equation

Research on the biomechanical behavior of soft tissues has drawn a lot of recent attention due to its application in tumor pathology, rehabilitation, surgery and biomaterial implants. In this study a finite element (FE) model is applied to represent soft tissues and phantoms with complex geometry and heterogeneous material properties. A solid 3D mixed u-p element S8P0 (8-node for displacement and 1-node for internal pressure) is implemented to capture the near-incompressibility inherent in soft tissues. A dynamic analysis of soft tissues’ response to excitation is explored in which, the second order differential equation representing the soft tissues in FE necessitates a time-consuming numerical solution procedure. Moreover, the second-order representation is complicated in estimating the tissue mechanical properties by inverse procedure. Thus, a state space (SS) model is used to equivalently represent soft tissues by transforming the second-order differential equation into a system of linear first-order differential equations. The linear and time-invariant SS representation of soft tissues for general dynamic analysis can reduce the computational cost and a provide framework for the “forward” simulation and “inverse” identification of soft tissues.

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