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wave equation (redirected fromSolving the wave equation) Thesaurus Encyclopedia wave equation n. 1.A differential or partial differential equation used to represent wave motion. 2.The fundamental equation of wave mechanics. American Heritage® Dictionary of the English Language, Fifth Edition. Copyright...
We explore a new asymptotic-numerical solver for the time-dependent wave equation with an interaction term that is oscillating in time with a very high frequency. The method involves representing the solution as an asymptotic series in inverse powers of the oscillation frequency. Using the new ...
Numerical methods based on finite differences for solving the wave equation are prone to various errors, a challenge that also applies to the semi-discrete case of a recently proposed quantum algorithm that preserves continuous time while discretizing space into a quantum state vector. The inherent ...
The aim of this thesis is implementation of algorithm for numerical solution of the wave equation on graphics processing unit. We used Euler and 4th order Runge-Kutta method. The methods differ in calculation complexity, numerical accuracy and numerical stability. Algorithms were implemented on CUDA ...
This package not only provides a numerical framework for solving the wave equation, but it also allows the gradient of the solutions to be computedautomaticallyvia pytorch's automatic differentiation framework. This gradient computation is equivalent to the adjoint variable method (AVM) that has recent...
Use C=VC′ to obtain the coefficients of basis, construct the final wave function. Example: Infinite potential box. [Math Processing Error]V(x)={0,x∈[−1,1]∞,otherwise The analytical solution is: \psi_n(x) = \left\{ \begin{aligned} & \cos(k_n x),\quad n{\rm{\, \, ...
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[6] equations, respectively. The KP equation, describing non-linear wave motion, has two forms (known as KPI and KPII) which differ in one particular sign appearing in the equation. The choice of the sign depends on the relative magnitude of the gravitational forces and the surface tension....
inverse problems; wave equations; deep learning; physics-informed neural networks; radial basis functions MSC: 35D35; 65M321. Introduction The wave equation is fundamental for modeling wave propagation phenomena, such as sound, light, and water waves, across various scientific and engineering fields ...