Convergence Example Problems Analysis Collocation Discretization of 1D Equation-The Matix One column for each density value x-x1S′… x.-xdS x xo x.-x1S′ ∫x-x1 nn yIx 0 One row for each collocation point SMA+HPC⊙2003M Discretization Convergence Theory 10
Convergence Numerical Results with Increasing n Analysis 25 n=40 15 10 n 0 n=20 15 20 Answers Are Getting Worse!!! 0.5 0.5 SMA+HPC⊙2003M Discretization Convergence Theory 11
Convergence Example Problems Analysis 1D Second Kind equation (a)=0(2)+门1-a()dsy∈[-1,1 The potential is given The density must be computed 平(x)=x3-x o(x is unknown 03 3 SMA+HPC⊙2003M Discretization Convergence Theory 12
Convergence Example Problems Analysis Collocation Discretization of 1D Equation 业(x)=0(x)+/1|e-xa(a)dsm∈[-1,1 Centroid Collocated Piecewise Constant Scheme Ro 业(x)=mi+∑=10nm312-ds SMA+HPC⊙2003M Discretization Convergence Theory 13