Laplace's equation

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Laplace's equation

[lə′pläs·əz i‚kwā·zhən]
(acoustics)
An equation for the speed c of sound in a gas; it may be written c = √(γ p /ρ), where p is the pressure, ρ is the density, and γ is the ratio of specific heats.
(mathematics)
The partial differential equation which states that the sum of all the nonmixed second partial derivatives equals 0; the potential functions of many physical systems satisfy this equation.
References in periodicals archive ?
The Laplace equation (2.5) for the potential [[??].sub.3] = [U.sub.3]-[U.sub.0] follows from the Laplace equation for [U.sub.3] and the fact that [[nabla].sup.2][U.sub.0] = 0.
The numerical solution of the Laplace equation requires the definition of the electrochemical parameters of the anode, the cathode, and the electrolyte in a 1M HCl electrolyte whose characteristics are cited in the Table 5 [16].
Here we introduce the solution of 2D Laplace equation with Dirichlet conditions in order to declare the basic idea of the method.
The CTM used to deal with the Laplace equation in the two-dimensional cylindrical coordinate system.
Green's function of Laplace equation is [mathematical expression not reproducible], where C is the boundary curve of plane closed area D and [d.sub.s] is arc differential [18].
Equation (89) agrees with the representation of the static electric field derived from the representation of the Laplace equation for the electrostatic potential [phi] and its normal derivative [partial derivative][phi]/[partial derivative]n = [rho]/[epsilon].
HAM has been applied successfully to obtain the series solution of various types of linear and nonlinear differential equations such as the viscous flows of non-Newtonian fluids [3-13], the KdV-type equations [14-16], nanoboundary layer flows [17], nonlinear heat transfer [18, 19], finance problems [20, 21], Riemann problems related to nonlinear shallow water equations [22], projectile motion [23], Glauert-jet flow [24], nonlinear water waves [25], ground water flows [26], Burgers-Huxley equation [27], time-dependent Emden-Fowler type equations [28], differential difference equation [29], difference equation [30], Laplace equation with Dirichlet and Neumann boundary conditions [31], and thermal-hydraulic networks [32].
According to quasistatic approach, the electrical potential distribution within the sample can be computed using the following Laplace equation:
We notice that (38) is the local fractional Laplace equation (see [21, 23]).