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Fixed discrete Laplace operator equation #12

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Fixed discrete Laplace operator equation #12

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4 changes: 2 additions & 2 deletions chapter12_deterministic/04_turing.md
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Expand Up @@ -69,7 +69,7 @@ V = np.random.rand(size, size)

6. Now, we define a function that computes the discrete Laplace operator of a 2D variable on the grid, using a five-point stencil finite difference method. This operator is defined by:

$$\Delta u(x,y) \simeq \frac{u(x+h,y)+u(x-h,y)+u(x,y+h)+u(x,y-h)-4u(x,y)}{dx^2}$$
$$\Delta u(x,y) \simeq \frac{u(x+h,y)+u(x-h,y)+u(x,y+h)+u(x,y-h)-4u(x,y)}{dh^2}$$

We can compute the values of this operator on the grid using vectorized matrix operations. Because of side effects on the edges of the matrix, we need to remove the borders of the grid in the computation:

Expand Down Expand Up @@ -152,7 +152,7 @@ $$\begin{align*}

We first use the following scheme for the discrete Laplace operator:

$$\Delta u(x,y) \simeq \frac{u(x+h,y)+u(x-h,y)+u(x,y+h)+u(x,y-h)-4u(x,y)}{dx^2}$$
$$\Delta u(x,y) \simeq \frac{u(x+h,y)+u(x-h,y)+u(x,y+h)+u(x,y-h)-4u(x,y)}{dh^2}$$

We also use this scheme for the time derivative of $u$ and $v$:

Expand Down