Partial differential equations can be clasified into parabolic , elliptic, and hyperbolic equations. In this article, we discuss the correspondence between parabolic and elliptic equations of the heat equation as seen from the heat flow. Suppose u states thetemperature on the object. If the two-dimensional heat equation is not affected by the times, the heat flow in steady state and parabolic equations become elliptic equations. To solve the heat equation, we can be used with the finite difference method and thealternating direction implicit.
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