c) Given the central difference approximation: \frac{\partial^{2} u(x, t)}{\partial x^{2}} \simeq \frac{u(x+h, t)-2 u(x, t)+u(x-h, t)}{h^{2}} use this expression along with the answer from part b) to discretise the partial differential equation. \frac{\partial u}{\partial t}=c \frac{\partial^{2} u}{\partial x^{2}} Take a step size of h in the x direction and k in t direction. Your answer should have-the form: w_{i j+1}=\lambda w_{i+1 j}+(1-2 \lambda) w_{i j}+\lambda w_{i-1 j} \text { where } w_{i j}=u\left(x_{i}, t_{j}\right)

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