Chemical Engineering Numerical Methods - Partial Differential Equation Experiments

PDE: Hyperbolic Equation

a2∂2u∂x2−∂2u∂t2=0 a^2 \frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial t^2} = 0 25∂2u∂x2−∂2u∂t2=0 25 \frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial t^2} = 0 when u(0,t)=0, u(5,t)=0, u(x,0)=x4(5−x) when\ u(0,t)=0,\ u(5,t)=0,\ u(x,0)=x^4(5-x) by initial condition   ∂u∂y=0 by\ initial\ condition\ \ \ \frac{\partial u}{\partial y} = 0 Find the distribution of u at x=1 and t = 0.2
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a2∂2u∂x2−∂2u∂t2=0 a^2 \frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial t^2} = 0 9∂2u∂x2−∂2u∂t2=0 9 \frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial t^2} = 0 when u(0,t)=0, u(5,t)=0, u(x,0)=x4(5−x) when\ u(0,t)=0,\ u(5,t)=0,\ u(x,0)=x^4(5-x) by initial condition   ∂u∂y=0 by\ initial\ condition\ \ \ \frac{\partial u}{\partial y} = 0 Find the distribution of u at x=2 and t = 0.33
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