Chemical Engineering Numerical Methods - Partial Differential Equation Experiments

PDE: Parabolic equation - explicit method

∂2u∂x2=a∂u∂t \frac{\partial^2 u}{\partial x^2} = a \frac{\partial u}{\partial t} ∂2u∂x2=3∂u∂t \frac{\partial^2 u}{\partial x^2} = 3 \frac{\partial u}{\partial t} when u(0,t)=0, u(4,t)=0, u(x,0)=x(4−x) when\ u(0,t)=0,\ u(4,t)=0,\ u(x,0)=x(4-x) h=1 h = 1 λ=0.25 \lambda = 0.25 Find the distribution of u at x=1 and t = 0.75
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∂2u∂x2=a∂u∂t \frac{\partial^2 u}{\partial x^2} = a \frac{\partial u}{\partial t} ∂2u∂x2=4∂u∂t \frac{\partial^2 u}{\partial x^2} = 4 \frac{\partial u}{\partial t} when u(0,t)=0, u(4,t)=0, u(x,0)=x(4−x) when\ u(0,t)=0,\ u(4,t)=0,\ u(x,0)=x(4-x) h=1 h = 1 λ=0.25 \lambda = 0.25 Find the distribution of u at x=2 and t = 1
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