Consider the following differential equation on the domain x < x < x2: du &...

 

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Consider the following differential equation on the domain x₁ < x < x2: ď² du & (2) - (²) d dx dr² + cu = f, 4 where a, b, c and f are known functions of r, and a(x), b(x), c(x) > 0Vx. Develop the variational formulation for the above differential equation in the form: Find u such that a(u, v) = L(v) Vv Identify the appropriate essential and natural boundary conditions. Show that a(.,.) is symmetric and positive definite. Formulate the min- imization problem corresponding to the variational formulation above for boundary conditions of your choice. Consider the following differential equation on the domain x₁ < x < x2: ď² du & (2) - (²) d dx dr² + cu = f, 4 where a, b, c and f are known functions of r, and a(x), b(x), c(x) > 0Vx. Develop the variational formulation for the above differential equation in the form: Find u such that a(u, v) = L(v) Vv Identify the appropriate essential and natural boundary conditions. Show that a(.,.) is symmetric and positive definite. Formulate the min- imization problem corresponding to the variational formulation above for boundary conditions of your choice.

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