A numerical method for determining the localized initial condition in the FitzHugh-Nagumo and Aliev-Panfilov models

2011 ◽  
Vol 35 (3) ◽  
pp. 105-112 ◽  
Author(s):  
I. A. Pavel’chak
Keyword(s):  
Numerical Method ◽  
Initial Condition ◽  
Localized Initial Condition

scholarly journals General Solution of Linear Partial Differential Equations Modeling Homogeneous diffusion-convection-reaction Problems with Cauchy Initial Condition

2019 ◽  
Vol 12 (2) ◽  
pp. 519-532
Author(s):  
Minoungou Youssouf ◽  
Bagayogo Moussa ◽  
Youssouf Pare
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Numerical Method ◽  
Initial Condition ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Diffusion Convection

In this paper, we propose the general solution of di¤usion-convection-reaction homogeneous problems with condition initial of Cauchy, using theSBA numerical method. This method is based on the combination of theAdomian Decompositional Method(ADM), the successive approximationsmethod and the Picard principle.

scholarly journals A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thuy Thi Thu Le ◽  
Loc Hoang Nguyen
Keyword(s):  
Parabolic Equation ◽  
Numerical Method ◽  
Quasilinear Parabolic Equation ◽  
Nonlinear Parabolic Equations ◽  
Cauchy Data ◽  
Initial Guess ◽  
Quasilinear Elliptic Equations ◽  
Initial Condition ◽  
True Solution ◽  
Highly Nonlinear

AbstractWe propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded domain. Although this problem is highly nonlinear, we do not require an initial guess of the true solution. The key in our method is the derivation of a boundary value problem for a system of coupled quasilinear elliptic equations whose solution is the vector function of the spatially dependent Fourier coefficients of the solution to the governing parabolic equation. We solve this problem by an iterative method. The global convergence of the system is rigorously established using a Carleman estimate. Numerical examples are presented.

scholarly journals NUMERICAL SOLUTION OF A MODEL FOR TURBULENT DIFFUSION

2013 ◽  
Vol 23 (10) ◽  
pp. 1350166 ◽  
Author(s):  
ERCILIA SOUSA
Keyword(s):  
Fractional Derivative ◽  
Numerical Method ◽  
Turbulent Diffusion ◽  
Riesz Space ◽  
Initial Condition ◽  
Riesz Fractional Derivative ◽  
First Order ◽  
Convergence Results ◽  
Implicit Numerical Method ◽  
Explicit Numerical Method

A model is considered for turbulent diffusion which consists of a Riesz space fractional derivative to describe the turbulent phenomenon and also includes advection and classical diffusion. We present a first order explicit numerical method and a second order implicit numerical method to solve our problem and prove convergence results for both methods, including the derivation of stability constraints needed for the explicit numerical method to converge. In the end, to give some insights into the phenomenon of turbulent diffusion described by the Riesz fractional derivative, we show the behavior of the solution when we consider a Gaussian initial condition.

ON THE DETERMINATION OF THE STOCHASTICITY THRESHOLD OF INVARIANT CURVES

1995 ◽  
Vol 05 (06) ◽  
pp. 1713-1719 ◽  
Author(s):  
ALESSANDRA CELLETTI ◽  
CLAUDE FROESCHLÉ
Keyword(s):  
Numerical Method ◽  
Canonical Transformation ◽  
High Accuracy ◽  
Initial Condition ◽  
Invariant Curves ◽  
Breakdown Threshold ◽  
Standard Mapping ◽  
Stochasticity Threshold ◽  
Integrable Mappings

We consider the problem of determining the stochasticity transition value in nearly-integrable mappings. We perform explicitly a canonical transformation, which conjugates the original mapping to an integrable one, up to a given order in the perturbing parameter. Then we derive a numerical evidence of the existence of an invariant curve associated with the transformed system and, correspondingly, to the original one. In the second part of the paper we implement a numerical method due to M. Hénon [Hénon] for the computation of the rotation number corresponding to a given initial condition. Following an idea of Laskar et al. [1992] and Laskar [1993], we determine with high accuracy the critical breakdown threshold of invariant curves for standard-mapping like systems which allows not only to test Hénon's method but also to compare our analytical results with an accurate numerical one. An application is also made about the accuracy of the leap frog method.

SOLUTION OF NEWEL-WHITEHEAD-SEGEL EQUATION USING CONFORMABLE FRACTIONAL SUMUDU DECOMPOSITION METHOD

2021 ◽  
Vol 21 (2) ◽  
pp. 479-486
Author(s):  
MOHAMED ELARBI BENATTIA ◽  
KACEM BELGHABA
Keyword(s):  
Numerical Method ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Condition ◽  
Adomian Decomposition ◽  
Sumudu Transform

In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-Segel equation subject to initial condition. This method is based d on the unification of conformable Sumudu transform (CST) and Adomian decomposition method (ADM), and then it is used to find the analytical solutions of linear-nonlinear fractional PDE’s. The test examples are given for illustration

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