The generalized finite difference method (GFDM) has been proved to be a good meshless method to solve several linear partial differential equations (pde's): wave propagation, advection鈥揹iffusion, plates, beams, etc. The GFDM allows us to use irregular clouds of nodes that can be of ...
In DNN, data sampling is another important factor for solving second-order or higher-order PDEs21,59,60,61. Latin hypercube sampling (LHS) filters the variance associated with the additive components of a transformation, and it is a powerful sampling method for data analysis in nearly every fie...
Fully nonlinear first-order equations are typically hard to solve without some conditions placed on the PDE. In this presentation we hope to present the Method of Characteristics, as well as introduce Calculus of Variations and Optimal Control. The content in the Method of Characteristics section is...
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Here, we use DFS-Net to simulate the time−dependent Klein–Gordon equation. This equation is a second-order nonlinear PDE closely related to many scientific fields, such as quantum, solid-state, and condensed matter physics41. The initial boundary value problem of the one−dimensional Klein...
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One of the obstacles which has hindered the study of this topic is that the constraints imposed by conformal symmetry have the form of second-order differential operators in momentum space. Determining the conformally invariant functions relevant for the scattering of particles thus requires to solve ...
A fourth order compact finite difference scheme is proposed for solving general second order steady partial differential equation (PDE) in two-dimension (2D) on geometries having nonuniform curvilinear grids. In this work, the main efforts are focused not only on nonorthogonal curvilinear grids but ...
For higher order PDEs, a finite element method (FEM) may be conveniently used for PDE solving and can give an accurate solution using extensive computational resources (Innerberger and Praetorius2023). Also, the multi-iteration solution limits practicality. As of now, solving PDEs is chiefly used...
PyPDE A Python library for solving any system of hyperbolic or parabolic Partial Differential Equations. The PDEs can have stiff source terms and non-conservative components. Key Features: Any first or second order system of PDEs Your fluxes and sources are written in Python for ease ...