Open formula of Runge–Kutta method for solving autonomous ordinary differential equation[J] . Maitree Podisuk.Applied Mathematics and Computation . 2006 (1)Podisuk, M. (2006) "Open formula of Runge-Kutta method
over ???, then there is a scheme for reducing the system of differential equations to an autonomous ordinary differential equation on one variable of the algebra; (2) a technique, previously introduced for solving differential equations over ???, is shown to work on the class mentioned in the...
Module 4: Differential Equations Search for: Solving the Logistic Differential EquationLearning Outcomes Draw a direction field for a logistic equation and interpret the solution curves Solve a logistic equation and interpret the resultsThe logistic differential equation is an autonomous differential equation...
In addition, four algorithms, two for non-autonomous ODEs (inolsp–inolwp) and another two for autonomous ODEs (iaolsp–iaolwp), have been implemented.References (23) J.I. Ramos et al. Piecewise-linearized methods for initial-value problems Applied Mathematics and Computation (1997) C.M. ...
Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as
Yang Z, Xu D (2008) Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays. Theor Comput Sci 403(1):3–10 Article MATH Google Scholar Li L, Huang L (2010) Equilibrium analysis for improved signal range model of delayed cellular neural networks. Neural...
Mukhopadhyay and Banerjee19 proposed a chaotic multi-group particle swarm optimization (CMS-PSO) to estimate the unknown parameters of an autonomous chaotic laser system. Duan et al.20 designed an improved particle swarm algorithm with nonlinear adjustment of inertia weights to improve the coupling ...
J. Solution existence for non-autonomous variable-order fractional differential equations. Math. Comput. Model. 55, 1106–1117. https://doi.org/10.1016/j.mcm.2011.09.034 (2012). Article MathSciNet Google Scholar Samko, S. G. & Ross, B. Integration and differentiation to a variable ...
Systems of differential equations that correspond to first order exact equations are called Hamiltonian systems. For the two-dimensional autonomous system {dx/dt=f(x,y)dy/dt=g(x,y) assume that f, g, ∂f/∂x, ∂f/∂y, ∂g/∂x, and ∂g/∂y are continuous on a region ...
(1). As is well-known in the study of ordinary differential equations, let x(t) be a solution of the autonomous system, x˙=F(x(t)),t≥0,x(0)=x0isgiven,and we define a flow ϕ which is the mapping ϕx0(t):=x(t). Then, for any s, t ≥ 0 the flow ϕ ...