Exact differential equation is a type of differential equation there exists a function of two variables with continuous partial derivatives with integrating factor.
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 ...
In line with the previous section, we study the linear convergence in terms of dual objective value and we derive some formulas for linear convergence rate by using performance estimation. It is noteworthy to mention that the term "Q-linear convergence" is also employed to describe the linear ...
A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variablexand the temporal variablet, and they are exponentially asymptotic to integer multiples of 2π asx→ ±∞. The solution...
It is noteworthy that, although we assume the absence of self-loops so as to derive the simplified formulas (equation (5)) and (equation (6)), they are still valid in the presence of a small fraction of self-loops, insofar as the self-loops do not violate the dominations of 0 and ...
In this system, each cubic equation is solved using Cardano's formulas. The method proposed in this work preserves the positivity, the boundedness and the monotonicity of approximations, as well as the constant solutions of the continuous model. The simulations provided in this work show a good ...
The method of the inverse scattering problem is used to solve the Cauchyproblem for the Korteweg-deVries equation with initial data of step type: , . Formulas are obtained for transforming the scatteringdata with respect to the time, mak... EJ Hruslov - 《Mathematics of the Ussr Sbornik》 ...
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 ...