Consider the following example of the heat equation: Uf = 3 . · Uzz, u (x, 0) = 4 · (2 – x) · æ², u (0, t) = 0, u (2, t) = 0. Assume we discretize with five nodes and that we choose At = 1.0. Use the Crank-Nicholson method (Lecture 28) to find the solution on the interior nodes after 1 step (enter your answer to 3dps).

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.