Ordinary Differential Equation Research Papers (original) (raw)
An innovative technique of NPCS are being used in engineering, computer sciences and natural sciences field to solve PDEs and ODEs Problems. There are many problems not having exact solution or not much stable and convergent exact... more
An innovative technique of NPCS are being used in engineering, computer sciences and natural sciences field to solve PDEs and ODEs Problems. There are many problems not having exact solution or not much stable and convergent exact solution, to solve such problem one apply different approximation, iterative and many other methods. The developed technique is one of them and implemented on some homogeneous parabolic PDEs of different dimensions and getting results will compare with exact solution and one other existing method, by tabular and graphically as well. Graphs and Mathematical result are found by using MATHEMATICA. Copyright(c) The Authors
In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed. We use two different approaches, namely the Riccati-Bernoulli... more
In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed. We use two different approaches, namely the Riccati-Bernoulli sub-ordinary differential equations and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, and rational stochastic solutions. Due to the significance of the Davey-Stewartson equations in the theory of turbulence for plasma waves, the discovered solutions are useful in explaining a number of fascinating physical phenomena. Moreover, we illustrate how the fractional derivative and Brownian motion affect the exact solutions of the SFDSEs using MATLAB tools to plot our solutions and display a number of three-dimensional graphs. We demonstrate how the multiplicative Brownian motion stabilizes the SFDSE solutions at around zero.
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of... more
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational comple...
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of... more
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational comple...
An open reactive system is modelled by coupling the chemical kinetics to diffuse transport. This system operates far from the regime of linear irreversible thermodynamics. The kinetics correspond to a certain region in the parameter space... more
An open reactive system is modelled by coupling the chemical kinetics to diffuse transport. This system operates far from the regime of linear irreversible thermodynamics. The kinetics correspond to a certain region in the parameter space of the Oregonator for which two symmetrybreakdowns occur: a) A periodic orbit contained in an unstable manifold of the phase space. This solution is invariant under time-translations generated by a period. b) A spatial stationary dissipative structure. This solution is invariant under a subgroup of the space symmetry group. The initial time periodicity of the system is followed by a spatial pattern. The restriction to the center manifold in the phase space allows to reduce an infinitedimensional problem for the bifurcation of a semiflow to a finite dimensional system of ordinary differential equations. The ranges in the control concentrations for this dynamics is found in accord with the experimental values. We also demonstrate that if the vessel i...
- by Sándor Fridli
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The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and the density of the operator... more
The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and the density of the operator range generated by the considered problem is proved by using the functional analysis method. Subsequently, by applying an iterative process based on the obtained results for the linear problem, the existence, uniqueness of the weak solution of the nonlinear problems is established.
The influence of thermophoretic transport of Al2O3 nanoparticles on heat and mass transfer in viscoelastic flow of oil-based nanofluid past porous exponentially stretching surface with activation energy has been examined. Similarity... more
The influence of thermophoretic transport of Al2O3 nanoparticles on heat and mass transfer in viscoelastic flow of oil-based nanofluid past porous exponentially stretching surface with activation energy has been examined. Similarity technique was employed to transform the governing partial differential equations into a coupled fourth-order ordinary differential equations which were reduced to a system of first-order ordinary differential equations and then solved numerically using the fourth-order Runge-Kutta algorithm with a shooting method. The results for various controlling parameters were tabulated and graphically illustrated. It was found that the thermophoretic transport of Al2O3 nanoparticles did not affect the rate of flow and heat transfer at the surface but it affected the rate of mass transfer of the nanofluid which decayed the solutal boundary layer thickness. This study also revealed that activation energy retards the rate of mass transfer which causes a thickening of ...
In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution of fractional order partial... more
In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution of fractional order partial differential equations (FOPDEs) in three dimensions. The fractional derivatives have been taken in the Caputo sense. As a particular example, we consider a fractional order three dimensional homogeneous heat equation and apply the extended notion for its analytical solution. We then perform numerical simulations to support and verify our analytical calculations. We use Fox-function theory to present the derived solution in compact form.
Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations. KP WALKER, AD FREED 1991. New methods for integrating systems of stiff, nonlinear, first order, ordinary differential ...
Ordinary linear differential equations containing small parameter ϵ \epsilon are investigated in regard to the existence of solutions in power series of the parameter. A new perturbation technique is developed which yields solutions more... more
Ordinary linear differential equations containing small parameter ϵ \epsilon are investigated in regard to the existence of solutions in power series of the parameter. A new perturbation technique is developed which yields solutions more convenient for computation than comparable solutions obtained by making the usual series expansion in the small parameter. The new method is applied to second and fourth order differential equations in normal form and it is shown that the method yields asymptotic solution for small ϵ \epsilon . Conditions needed for successful application of the method are discussed and a typical solution is obtained. Comparison of numerical results with an exact solution and with an ordinary perturbation solution indicates the usefulness of the technique.
In this paper, we will use analytical methods for solving the fundamental element of a reaction diffusion model in ecology. The model denotes an interaction between two species which describe ecological predations, and mathematically is... more
In this paper, we will use analytical methods for solving the fundamental element of a reaction diffusion model in ecology. The model denotes an interaction between two species which describe ecological predations, and mathematically is defined as a system of partial differential equations with initial and boundary conditions. Symmetry Lie group methods are used to transform this model into a system of ordinary differential equations, then this system solved by generalized tanh function method when there exists a small parameter appear in one of the equation.
An anatomical dynamic model consisting of three body segments, femur, tibia and patella, has been developed in order to determine the three-dimensional dynamic response of the human knee. Deformable contact was allowed at all articular... more
An anatomical dynamic model consisting of three body segments, femur, tibia and patella, has been developed in order to determine the three-dimensional dynamic response of the human knee. Deformable contact was allowed at all articular surfaces, which were mathematically represented using Coons’ bicubic surface patches. Nonlinear elastic springs were used to model all ligamentous structures. Two joint coordinate systems were employed to describe the six-degrees-of-freedom tibio-femoral (TF) and patello-femoral (PF) joint motions using twelve kinematic parameters. Two versions of the model were developed to account for wrapping and nonwrapping of the quadriceps tendon around the femur. Model equations consist of twelve nonlinear second-order ordinary differential equations coupled with nonlinear algebraic constraint equations resulting in a Differential-Algebraic Equations (DAE) system that was solved using the D_ifferential/A_lgebraic S_ystem S_ol_ver (DASSL) developed at Lawrence L...