{"title":"Introduction to Boundary Value Problems","authors":"D. Gleich","doi":"10.1142/9789813274037_0001","DOIUrl":"https://doi.org/10.1142/9789813274037_0001","url":null,"abstract":"1 # We use a grid representation of the function u(x) on [0, 1] 2 # so we divide [0, 1] up into N + 1 increments of 1/N each. 3 4 N = 10 5 xgrid = collect(0:1/N:1) 6 7 # This means that u is a vector with n = N+1 elements, 8 # but two of them are fixed at alpha and beta. 9 10 n = length(xgrid) 11 12 example_u = zeros(n); 13 example_u[1] = 1 # suppose alpha = 1 14 example_u[end] = 1/2 # suppose beta = 1/2 15 16 example_u[2:end-1] = 1.06-1*(xgrid[2:end-1]-0.25).^2; 17 18 plot(xgrid, example_u)","PeriodicalId":140610,"journal":{"name":"Ordinary Differential Equations and Boundary Value Problems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133582558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}