an undetermined constant in a differential equation having the same value during all changes in the values of the variables. See also:Arbitrary,Constant Webster's Revised Unabridged Dictionary, published 1913 by
[translate] aLuxury Ming 豪华Ming[translate] aPlants give off a bad smell 植物释放难闻的气味[translate] aIf the solution containing arbitrary constant differential equation 如果包含任意恒定的微分方程的解答[translate]
An arbitrary constant in computer science refers to a constant value that can be determined based on the given initial conditions or constraints in a mathematical equation or algorithm. AI generated definition based on: Theory and Applications of Numerical Analysis (Second Edition), 1996 ...
Of critical importance within the block representation are the volume and geometric shape of the block, since a block is generally defined as a rigid body characterized by a domain of constant volume and mass. In consideration of the fact that all bodies are more or less deformable, the first...
The solvability of equations (11) follows from the fact that, after the Laplace transform, the N coupled equations reduce to a single first-order ordinary differential equation in the Laplace transform of v, which can always be solved analytically (see Methods). This model is a special case ...
In the first example, we adjusted the coefficients of the three differential kernels to −0.1, 1, and −0.3. To verify the accuracy of the solution, we provide the left and right sides of the equationg(t) = s1Kg(t) - s12Kx(t), respectively, as shown in Fig.3b. The ...
Tatar, N-e: Arbitrary decay in linear viscoelasticity. J Math Phys. 52, 013502 (2010) 26. Wu, ST: Blow-up of solutions for an integro-differential equation with a nonlinear source. Electron J Diff Equ. 45, 1–9 (2006) 27. Wu, ST: General decay of solutions for a viscoelastic ...
The method uses a constant velocity contour line in a typical cross-section of the duch as an independent variable. The amplitude of the oscillatory velocity is then obtained from an ordinary integro-differential equation. Several examples of a practical nature are given, with some that have not...
In this paper, we consider the integro-differential equation u_{tt}-M(\|\nabla u\|^{2}_{2})\Delta u+ \int_{0}^{t} g(t-\tau)\Delta u(\tau)\, d\tau+ u_{t}=f(u), (x,t)\in\Omega\times(0,T), with initial and Dirichlet boundary conditions. Under suitable assumptions ...
For this purpose, block-pulse functions (BPFs) as a set of piecewise constant orthogonal functions are used. By the BPFs vector forms and operational matrix of integration, solving the differential equation is reduced to solve a linear system of algebraic equations. Some problems are numerically ...