Exact Differential Equation: A differential equation that can be written in the form M(t,y) dt + N(t,y) dy = 0 where M(t,y) dt+N(t,y) dy = (∂f/∂t)(t,y)dt+(∂f/∂y)(t,y)dy for some function z = f(t,y) is called an exact differential equation. ...
A difference approximation to a linear ordinary differential operator can in many cases be represented as an integral. If the integral is evaluated exactly, one obtains an exact method for obtaining a table of values of the solution to an ordinary differential equation. Many well-known methods ...
Formulas MathBrowse all » Wolfram Community » Wolfram Language » Demonstrations » Connected Devices » Exact Differential Equations Differential Equation General Solution Same as the above multiplied by the integrating factor . Integrating Factors In solving "exactable" ordinary differential...
This paper points out several exact travelling wave solutions for ( 1 + 1 ) -dimensional Ito integro-differential equation via the Riccati鈥揃ernoulli sub-ODE approach. We also aim to develop a numerical solution of the respective equation using central finite difference formulas. The stability ...
We analytically derive the exact formulas for the critical coupling strengths at different time delays in both directions of increasing (forward) and decreasing (backward) coupling strengths. We find that time-delay does not affect the transition for the backward direction but can shift the ...
A proof that our formulas (40)–(41) agree with (47) as long as u is smooth enough is given in the work by Thaler [23]. Acknowledgments AET would like to thank Patrick Bardsley, Andrej Cherkaev, Elena Cherkaev, Fernando Guevara Vasquez, and Hyeonbae Kang for helpful discussions. The ...
Ordinary Differential Equations Partial Differential Equations on Manifolds Waves, instabilities and nonlinear plasma dynamics 1Introduction We consider the dispersionless Veselov-Novikov equation (dVN) [11] written in the form \begin{aligned} u_{txy} = (u_{xx}u_{xy})_x+(u_{xy}u_{yy})_y...
Our method is to propose a two species reaction network whose kinetics can be described by a system of linear differential equations. We solve this system (an initial value problem) to obtain a harmonic oscillator with closed form formulas that relate OCs to parameters of the reaction network. ...
We perform a complete spectral analysis of the linear three-dimensional Boltzmann BGK operator resulting in an explicit transcendental equation for the eig
In the described way for the differential equation (2.1) withthe initial conditions (2.2)and boundary conditions of the third kind, we can find first-kind boundary conditions (2.3) Exact difference schemes for hyperbolic equations349using the formulasμ1(t) =...