👉 General Partial Differential Equations (GPDEs) are a class of mathematical equations that describe how quantities change over space and time, incorporating both spatial derivatives (like gradients and curvature) and temporal derivatives. They extend ordinary partial differential equations (PDEs), which deal with functions of one or more independent variables and their derivatives, by allowing these derivatives to depend on multiple variables simultaneously. This makes GPDEs particularly useful for modeling complex physical phenomena such as fluid dynamics, heat conduction, and electromagnetic fields, where interactions between space and time are crucial. Solutions to GPDEs often require advanced mathematical techniques, including separation of variables, Fourier analysis, and numerical methods, to find functions that satisfy both the equation and specified boundary conditions.
