# This file is part of the Test Set for BVP solvers # # http://www.dm.uniba.it/~bvpsolvers/ # # Problem bvpT9 # ODE of dimension 2 # # DISCLAIMER: see # http://www.dm.uniba.it/~bvpsolvers/testsetbvpsolvers # # bvpT9<- function(){ prob<- function(){ fullnm <- 'Problem bvpT9' problm = 'bvpT9' typebvp = 'SPBVP' neqn = 2 nlbc = 1 aleft = -1.0e0 aright = 1.0e0 numjac = FALSE numbcjac = FALSE linear = TRUE Rpar<-c(0.5) Ipar<-0 ms <- rep(1,neqn) return(list(fullnm=fullnm,problm=problm,typebvp=typebvp,neqn=neqn, nlbc=nlbc,ms=ms,aleft=aleft,aright=aright,Rpar=Rpar,Ipar=Ipar, numjac=numjac,numbcjac=numbcjac,linear=linear)) } init <- function(neqn,ms,aleft,aright) { givmsh = FALSE givey = FALSE nmsh = 11 xguess = seq(aleft,aright,by=(aright-aleft)/(nmsh-1)) yguess <- NULL for (i in 1:neqn) for (j in 1:ms[i]) yguess <- rbind(yguess,rep(0,nmsh)) return(list(givmsh=givmsh,givey=givey, nmsh=nmsh,xguess=xguess,yguess=yguess)) } feval = function(x,y,eps,Rpar,Ipar){ f <- c(y[2], -(4.0e0*x*y[2]+2.0e0*y[1])/(eps+x^2)) return(list(f)) } jeval = function(x,y,eps,Rpar,Ipar){ dfy <- matrix( nrow=2,ncol=2,byrow = TRUE, data = c( 0, 1, -2.0e0/(eps+x^2), -4.0e0*x/(eps+x^2))) return((dfy)) } bceval <- function(i, y, eps,Rpar,Ipar) { if (i == 1) return(y[1]-1/(1+eps)) if (i == 2) return(y[1]-1/(1+eps)) } dbceval <- function(i, y, eps,Rpar,Ipar) { if (i == 1) return(c(1, 0)) if (i == 2) return(c(1, 0)) } setoutput<- function(neqn,plotsol=NULL){ solref =TRUE if (is.null(plotsol)){ nindsol = neqn indsol = 1;neqn } else{ nindsol = length(plotsol) indsol = plotsol } return(list(solref=solref,nindsol=nindsol,indsol=indsol)) } esolu <- function(X,parms,Rpar,Ipar){ lambda=parms Exact =matrix( c( 1.0e0/(X*X+lambda), -(2*X)/(X^2 + lambda)^2), ncol=2,nrow=length(X),byrow=FALSE) return(Exact=Exact) } return(list(prob=prob,init=init,feval=feval,jeval=jeval,bceval=bceval,dbceval=dbceval,setoutput=setoutput,esolu=esolu)) }