Solution of a nonlinear time-delay model in biology via semi-analytical approaches

DOI10.1016/j.cpc.2010.03.014zbMath1219.65062OpenAlexW1974988984MaRDI QIDQ547016

Rezvan Salehi, Mehdi Dehghan

Publication date: 30 June 2011

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2010.03.014

zbMATH Keywords

numerical examplesdelay differential equationpopulation dynamicsAdomian decomposition methodvariational iteration methoddelay logistic equationsemi-analytic approach

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Numerical methods for functional-differential equations (65L03) Functional-differential inequalities (34K38)

Related Items (51)

The first integral method for constructing exact and explicit solutions to nonlinear evolution equations ⋮ Two reliable methods for solving the Volterra integral equation with a weakly singular kernel ⋮ Residue harmonic balance solution procedure to nonlinear delay differential systems ⋮ An accurate Chebyshev pseudospectral scheme for multi-dimensional parabolic problems with time delays ⋮ An effective numerical method for solving fractional pantograph differential equations using modification of hat functions ⋮ A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area ⋮ Solving a laminar boundary layer equation with the rational Gegenbauer functions ⋮ Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution ⋮ A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation ⋮ General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis ⋮ A semi-linear delayed diffusion-wave system with distributed order in time ⋮ A shifted Legendre method for solving a population model and delay linear Volterra integro-differential equations ⋮ Method of time-discretization to a multiterm nonlinear retarded differential equation ⋮ Application of homotopy perturbation method to solve two models of delay differential equation systems ⋮ Simplified reproducing kernel method for fractional differential equations with delay ⋮ Application of semi‐analytical methods for solving the Rosenau‐Hyman equation arising in the pattern formation in liquid drops ⋮ Approximate analytical solution to time fractional nonlinear evolution equations ⋮ A semi‐analytical technique for the solution of differential‐algebraic equations and applications in flow of an incompressible viscous fluid ⋮ Homotopy Padé method for solving second-order one-dimensional telegraph equation ⋮ Fuzzy fractional functional differential equations under Caputo gH-differentiability ⋮ Simultaneous partial slip and thermal-diffusion and diffusion-thermoeffects on steady MHD convective flow due to a rotating disk ⋮ Successive linearization analysis of the effects of partial slip, thermal diffusion, and diffusion-thermo on steady MHD convective flow due to a rotating disk ⋮ Homotopy analysis method for MHD viscoelastic fluid flow and heat transfer in a channel with a stretching wall ⋮ Approximation methods for solving fractional equations ⋮ On the solutions of a system of linear retarded and advanced differential equations by the Bessel collocation approximation ⋮ A modified spectral method for solving operator equations ⋮ Fractional variational problems depending on indefinite integrals and with delay ⋮ On a class of non-linear delay distributed order fractional diffusion equations ⋮ Reproducing kernel method to solve fractional delay differential equations ⋮ Solution of time-varying delay systems using an adaptive collocation method ⋮ Mixed finite difference and Galerkin methods for solving Burgers equations using interpolating scaling functions ⋮ Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses ⋮ The general Jacobi matrix method for solving some nonlinear ordinary differential equations ⋮ Collocation method for the numerical solutions of Lane–Emden type equations using cubic Hermite spline functions ⋮ A differential transformation approach for solving functional differential equations with multiple delays ⋮ On the solutions of nonlinear higher-order boundary value problems by using differential transformation method and Adomian decomposition method ⋮ Numerical and analytical investigations for neutral delay fractional damped diffusion-wave equation based on the stabilized interpolating element free Galerkin (IEFG) method ⋮ Rational pseudospectral approximation to the solution of a nonlinear integro-differential equation arising in modeling of the population growth ⋮ ANALYTICAL TREATMENT OF SOME PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MATHEMATICAL PHYSICS BY USING THEExp-FUNCTION METHOD ⋮ The stability and control of fractional nonlinear system with distributed time delay ⋮ Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations ⋮ Nonlinear partial differential equations in mathematics and physics ⋮ Multistep finite difference schemes for the variable coefficient delay parabolic equations ⋮ Bifurcation of the periodic motion in nonlinear delayed oscillators ⋮ Numerical Solution of Second-Order Linear Delay Differential and Integro-Differential Equations by Using Taylor Collocation Method ⋮ Fast spectral collocation method for solving nonlinear time-delayed Burgers-type equations with positive power terms ⋮ A solution to the Lane-Emden equation in the theory of stellar structure utilizing the Tau method ⋮ A simple time-delay memristor and its application in 2D HR neuron model ⋮ Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes ⋮ Four techniques based on the B-spline expansion and the collocation approach for the numerical solution of the Lane-Emden equation ⋮ A new study on delay fractional variational problems

Uses Software

• dde23

Cites Work

• A one-step subregion method for delay differential equations
• Solution of problems in calculus of variations via He's variational iteration method
• Chaos in the delay logistic equation with discontinuous delays
• Variational iteration method for solving the wave equation subject to an integral conservation condition
• The use of Adomian decomposition method for solving problems in calculus of variations
• Delay differential equations: with applications in population dynamics
• The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Padé technique
• An analytical solution for a nonlinear time-delay model in biology
• A nonlinear equation with piecewise continuous argument
• One-step collocation for delay differential equations
• Numerical solution of the Klein-Gordon equation via He's variational iteration method
• Solution of the fully fuzzy linear systems using the decomposition procedure
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• A 3(2) pair of Runge-Kutta formulas
• Numerical solution of a biological population model using He's variational iteration method
• A study on linear and nonlinear Schrödinger equations by the variational iteration method
• The decomposition method for initial value problems
• Variational iteration method for solving a generalized pantograph equation
• The variational iteration method for a reliable treatment of the linear and the nonlinear goursat problem
• Variational iteration method -- some recent results and new interpretations
• An approximation solution of a nonlinear equation with Riemann-Liouville's fractional derivatives by He's variational iteration method
• On the convergence of He's variational iteration method
• Solutions of singular IVPs of Lane-Emden type by the variational iteration method
• Solution of a model describing biological species living together using the variational iteration method
• Application of the Adomian decomposition method for the Fokker-Planck equation
• A review of the decomposition method in applied mathematics
• Strong contractivity properties of numerical methods for ordinary and delay differential equations
• Variational iteration method for delay differential equations
• Solving frontier problems of physics: the decomposition method
• The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model
• Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
• QMC methods for the solution of delay differential equations.
• Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications
• Numerical comparison of methods for solving parabolic equations
• Issues in the numerical solution of evolutionary delay differential equations
• The solution of coupled Burgers' equations using Adomian-Padé technique
• Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem
• Analysis of stability and Hopf bifurcation for a delayed logistic equation
• Parameter determination in a partial differential equation from the overspecified data
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Asymptotic methods for delay equations
• Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method
• A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity
• The use of variational iteration method and Adomian decomposition method to solve the Eikonal equation and its application in the reconstruction problem
• Estimation of Delays and Other Parameters in Nonlinear Functional Differential Equations
• The use of He's variational iteration method for solving the telegraph and fractional telegraph equations
• On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation
• Solution of a Parabolic Equation with a Time-Dependent Coefficient and an Extra Measurement Using the Decomposition Procedure of Adomian
• The numerical solution of the second Painlevé equation
• Solving a fourth-order fractional diffusion-wave equation in a bounded domain by decomposition method
• A seminumeric approach for solution of the Eikonal partial differential equation and its applications
• The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics
• Numerical method for non-linear wave and diffusion equations by the variational iteration method
• Interpolation for Runge–Kutta Methods
• An Asymptotic Analysis of the Delayed Logistic Equation when the Delay is Large
• A Delay Logistic Equation with Variable Growth Rate
• Numerical Solution of Laplace Equation in a Disk using the Adomian Decomposition Method
• A non-linear difference-differential equation.
• Variational iteration method for autonomous ordinary differential systems
• Solving DDEs in Matlab
• Approximate analytical solution of Blasius' equation

This page was built for publication: Solution of a nonlinear time-delay model in biology via semi-analytical approaches