Implement the finite element method for one-dimensional problems in Fortran, using continuous linear interpolation by parts in space. Implement Euler method explicit and implicit and Crank-Nicolson. Run examples that demonstrate that the method and program are correct.

(8.3a) au 22u at ax2 =f 00, (8.35) u(0,t)=u(it,t)=0 t>0, (8.3c) u(1,0)=u2(x) 00, (8.35) u(0,t)=u(it,t)=0 t>0, (8.3c) u(1,0)=u2(x) 0