Ordinary Differential Equations and Applied Dynamics Commons^™

Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable combination of homotopy perturbation method and Padé approximants to investigate the Flierl-Petviashivili (FP) equation. The approach introduces a new transformation necessary for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed homotopy perturbation method is applied to the reformulated first order initial value problem which leads the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm may …

A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the variational iteration method (VIM) for solving higher-order integro differential equations by converting the problems into system of integral equations. The proposed technique is applied to the re-formulated system of integro-differential equations. Numerical results show the accuracy and efficiency of the suggested algorithm. The fact that the VIM solves nonlinear problems without calculating Adomian’s polynomials is a clear advantage of this technique over the decomposition method.

Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a relatively new technique which is called the variational iteration decomposition method (VIDM) by combining the traditional variational iteration and the decomposition methods for solving higher dimensional initial boundary value problems. The proposed method is an elegant combination of variational iteration and the decomposition methods. The analytical results of the problems have been obtained in terms of convergent series with easily computable components. The method is quite efficient and is practically well suited for use in these problems. Several examples are given to verify the accuracy and efficiency of the proposed technique.

Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari

Applications and Applied Mathematics: An International Journal (AAM)

System of linear equations is applied for solving many problems in various areas of applied sciences. Fuzzy methods constitute an important mathematical and computational tool for modeling real-world systems with uncertainties of parameters. In this paper, we discuss about fully fuzzy linear systems in the form AX = b (FFLS). A novel method for finding the non-zero fuzzy solutions of these systems is proposed. We suppose that all elements of coefficient matrix A are positive and we employ parametric form linear system. Finally, Numerical examples are presented to illustrate this approach and its results are compared with other methods.

A Further Result On The Instability Of Solutions To A Class Of Non-Autonomous Ordinary Differential Equations Of Sixth Order, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our result includes and improves some well-known results in the literature.

Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm.

The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow

Articles and Preprints

We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.

Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits, and we characterize the dynamics in terms of the relaxation time and viscosity.

The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The adaptability principle of mechanical law and the scale-invariant principle of mechanical law in fractal space are proved by using parameter-space and scale-space transforms in renormalization groups.From the space-transform angle,the transform of mechanical law from fractal space to European space is the scale-invariant transform while the transform of mechanical law from European space to fractal space is the adaptability transform.Their deductions are that law of conservation of energy and vectorial resultant of force and displacement in fractal space hold the line in form and Carpinteri's dimensional formula of fractal space is also proved. Namely,the spilling dimension of volume in fractal …

Fractional Definite Integral, Yang Xiaojun

Xiao-Jun Yang

Fractional definite integral is that a value of the integral calculus over given interva1．Under the circumstance of fractional dimension，fractional definite integral is important to compute some value in given interva1．It is complied with starting introducing definition，the properties，leads into fractional integral function of definition and the properties，and then induces to basic theorems for fractional integral calculus

A Study Of Present Value Maximization For The Monopolist Problem In Time Scales, Keshav Prasad Pokhrel

Theses, Dissertations and Capstones

There are some mathematical characters in the abstract that will not transfer. Refer to the download to read full abstract.

General results for time scales with right dense points are established. A study of issues that arise when unifying (C) and (D) is included in the analysis

Blow-Up Behavior Of Solutions For Some Ordinary And Partial Differential Equations, Sarah Y. Bahk

Theses Digitization Project

There are two parts in this project. Part 1 the Riccati initial-value problem is looked at. Part 2 considers blow-up property solutions for the degenerate semilinear parabolic initial-boundary value problem.

Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades

Publications

Phototransduction is the process by which photons of light generate an electrical response in retinal rod and cone photoreceptors, thereby initiating vision. We compare the electrical response in salamander rods from increasingly more (spacialy) detailed models of phototransduction: 0-dimensional (bulk), 1-dimensional (longitudinal), 2-dimensional (axisymmetric), and 3-dimensional (with incisures). We discuss issues of finding physical parameters for simulation and validation of models, and also present some computational experiments for rods with geometry of mouse and human photoreceptors.