This result is central to the method of solving differential equations used in this chapter and also to the Laplace transform method of the next chapter. Example 14.3 A differential equation d2x/dt2+9x=f(t) is found to have a particular solution x = t /9 when f(t) = t and a ...
However, I wonder if there is a solution involving differential equations. I wish to integrate both sides, but do not know how: Divide both sides of f′(x)g(x)−f(x)g′(x)=cf′(x)g(x)−f(x)g′(x)=c by g2(x)g2(x) (c≠0c≠0 implies that g(x)≠0g(x)≠0), ...
The system of algebraic equations is solved by an implicit iterative method combined with Gauss elimination. A Mathematica module is designed for the purpose of testing and using the method. To illustrate the method, the equation of twisting a springy rod is solved. 2000 John Wiley & ...
By introducing a relaxation parameter, we derive a relaxed gradient based iterative algorithm for solving Sylvester equations. Theoretical analysis shows t... Q Niu,X Wang,Lin‐Zhang Lu - 《Asian Journal of Control》 被引量: 73发表: 2011年 Ant colony algorithm for solving fault location in dis...
2.2.1 CNNs for solving non-linear equations As per the work of Lagaris et al. (1998), the Differential Equations can be broken down into sub-components using the Dirichlet and Neumann expressions. By using neural networks (Lagaris et al. 1998), non-linear equations were solved up to the...
FTFD我们记:在 t=tn 时刻,位于 x=xj 上的函数值为 ujn 。其中时间和空间都是均匀的网格 (Δt,Δx) 。现采用时间向前差分(FT),空间向前差分(FD),则差分格式为: (4)ujn+1−ujnΔt+cuj+1n−ujnΔx=0 或写作 (5)un+1=(1+v)ujn−vuj+1n ...
The paper gives a new method for finding solutions of a nonlinear system of equations in a compact m -dimensional interval (rectangle). This method can be ... F Kálovics - 《Computing》 被引量: 7发表: 1992年 Low-temperature collisional quenching of NO A~2Σ~+(v′ = 0) by NO(X~...
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At times, evaluating a function in table form may be more useful than using equations. Here let us call the functionPP. Thedomainof the function is the type of pet and the range is a real number representing the number of hours the pet’s memory span lasts. We can evaluate the function...
\tilde x_{n+1}=x_n+\frac{1}{2}[f(x_n)+f(\tilde x_{n+1})]\Delta t(实际步骤) 这种方法比欧拉方法更准确,因为它在给定的步长\Delta t,倾向于一个较小的误差E=|x(t_n)-x_n|。在这两种情况下,该错误E\rightarrow0当t\rightarrow0,但改进的欧拉方法的误差减小得更快。可以证明欧拉法的...