Teaching the Logistic Growth Difference Equation Using Spreadsheets [PDF]
Spreadsheets in Education, 2010 The logistic growth difference equation is often used in biology to model population growth. The terms that satisfy the difference equation have many remarkable mathematical properties such as exhibiting chaotic behavior. Using spreadsheet modeling tools,
Fred J Rispoli +2 more
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Implicit methods for the simple wave equation [PDF]
, 1984 A family of finite difference methods is developed for the numerical solution of the simple wave equation. Local truncation errors are cal- culated for each member of the family and each is analyzed for stability.
Tirmizi, S I A, Twizell, E H
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A cubic spline technique for the one dimensional heat conduction equation [PDF]
, 1971 A new method is developed for the numerical solution of the heat conduction equation in one space dimension by replacing the space derivative with a cubic spline approximation and the time derivative with a finite- difference approximation. The method is
Whiteman, J R, Papamichael, N
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On the local dynamics of polynomial difference equations with fading stochastic perturbations [PDF]
, 2010 We examine the stability-instability behaviour of a polynomial difference equa- tion with state-independent, asymptotically fading stochastic perturbations. We find that the set of initial values can be partitioned into a stability region, an instability
Kelly, C. +3 more
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Modified finite-difference approximations near the singularitiy in the problem of motz [PDF]
, 1976 A simple, modified finite-difference method is described for solving Laplace's equation with boundary singularities of the infinite derivative type. Modified approximations for the derivatives of the Laplacian equation are employed near the singularity ...
Furzeland, RM, Crank, J
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Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes [PDF]
, 2011 We present a computational study of the solution of the Falkner-Skan equation (a third-order boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes.
Galeano, Carlos +5 more
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Fast computation of the nonlocal boundary condition in finite difference parabolic equation radiowave propagation simulations [PDF]
, 2008 Finite difference parabolic equation method (FD-PEM) codes using a nonlocal boundary condition to model radiowave propagation over electrically large domains, require the computation of time consuming spatial convolution integrals. For the first time, we
Mias, Christos
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Hexagonal vs. Rectilinear Grids for Explicit Finite Difference Schemes for the Two-dimensional Wave Equation [PDF]
, 2013 Finite difference schemes for the 2-D wave equation operating on hexagonal grids and the accompanyingnumerical dispersion properties have received little attention in comparison to schemes operating on rectilinear grids.
Stefan Bilbao +3 more
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Characteristics of Conservation Laws for Difference Equations [PDF]
, 2013 Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the ...
Hydon, PE +3 more
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Dynamics of a Rational Difference Equation
Advances in Difference Equations, 2010 The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn+1=(α+βxn+γxn-k)/(1+xn-k), n∈ℕ0, where the parameters
Wan-Tong Li, Lin-Xia Hu, Xiu-Mei Jia
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