Use the Galerkin method to solve the following boundaryvalue problem using a:

(a) oneterm approximation and

(b) twoterm approximation. Compare your results with the exact solution by plotting them on the same graph.

The approximate solution is split into two parts. The first term satisfies the given essential boundary conditions exactly, i.e., \(u(0)=1\) and \(u(1)=0\). The rest of the solution containing the unknown coefficients vanishes at the boundaries.

Transcribed Image Text:

du +x=0, 0x1 dr u(0)=1 Boundary conditions. u(1)=0