Answer Happy

1. Differentiate between strong formand weak form of the governing differential equation. 2. What is the need for numerical methods for finding the solution of partial differential equations? 3. What do you understand by natural boundary condition and essential boundary condition? 4. Using Galerkin's method, determine the linear and quadratic solution for the axial deformation of a tapered bar subjected to linearly varying axial load as shown in the following figure. Ао Axial load, 9(x) = CX AL Р EA(x) L The govering equation and the boundary conditions are as follows (symbols have their usual meaning): d du EA dx dx + cx = 0; + c 0<x<L AO - AL x = A(x) = 40 (L+(-1 + r)x)A, L L du(L) ErA, =P dx u(0) = 0; here =AJA. 5. Using Galerkin's method, find a cubic approximate solution of the following boundary value problem and compare its accuracy with that of the linear and quadratic solutions. x + 2xy +x = 1; 1<x< 2 u(1) = 2; u' (2) + 21(2) = 5