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partial differential equation |
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partial differential equationIn mathematics, an equation that contains partial derivatives, expressing a process of change that depends on more than one independent variable. It can be read as a statement about how a process evolves without specifying the formula defining the process. Given the initial state of the process (such as its size at time zero) and a description of how it is changing (i.e., the partial differential equation), its defining formula can be found by various methods, most based on integration. Important partial differential equations include the heat equation, the wave equation, and Laplace's equation, which are central to mathematical physics. |
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Since the early 1990s, researchers have also created computer nodels of snowflake growth that use partial differential equations to represent physical processes. The winning team used partial differential equations to optimize the equation. Luskin, The Computation of the Austenitic-Martensitic Phase Transition, Partial Differential Equations and Continuum Models of Phase Transition, Lecture Notes in Physics, Vol. |
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