Shock Capturing vs. Shock Fitting hocks when the shocks or di n the solution as regions of large gradients without having to give them any special treatment. If we use conservative schemes, the Lax-Wendroff theorem 's. will be to a weak solution We know tha reak solutions satisfy the jump conditions and therefore give the correct shock
1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension