# This file is part of the Test Set for BVP solvers # # http://www.dm.uniba.it/~bvpsolvers/ # # Problem bvpT33 # ODE of dimension 6 # # DISCLAIMER: see # http://www.dm.uniba.it/~bvpsolvers/testsetbvpsolvers # # Authors: # # Jeff R. Cash # (Department of Mathematics, Imperial College, London, England.) # Davy Hollevoet # (Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Belgium.) # Francesca Mazzia # (Dipartimento di Matematica, Universita' di Bari, Italy) # Abdelhameed Nagy Abdo # (Dipartimento di Matematica, Universita' di Bari, Italy) # (Dept. of Mathematics, Faculty of Sciences, Benha University,Egypt) bvpT33<- function(){ prob<- function(){ fullnm <- 'Problem bvpT33' problm = 'bvpT33' typebvp = 'SPBVP' neqn = 6 nlbc = 3 aleft = 0 aright = 1 numjac = FALSE numbcjac = FALSE linear = FALSE 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 = TRUE givey = TRUE 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(0.5,nmsh)) return(list(givmsh=givmsh,givey=givey, nmsh=nmsh,xguess=xguess,yguess=yguess)) } feval = function(x,y,eps,Rpar,Ipar){ f <- c(y[2], (y[1]*y[4]-y[3]*y[2])/eps, y[4], y[5], y[6], (-y[3]*y[6]-y[1]*y[2])/eps) return(list(f)) } jeval = function(x,y,eps,Rpar,Ipar){ dfy <- matrix( nrow=6,ncol=6,byrow = TRUE, data = c( 0, 1.0e0, 0, 0, 0, 0, y[4]/eps, -y[3]/eps , -y[2]/eps, y[1]/eps, 0, 0, 0, 0, 0, 1.0e0, 0, 0, 0, 0, 0, 0, 1.0e0, 0, 0, 0, 0, 0, 0, 1.0e0, -y[2]/eps, -y[1]/eps, -y[6]/eps, 0, 0, -y[3]/eps )) return((dfy)) } bceval <- function(i, y, eps,Rpar,Ipar) { if (i == 1) return(y[1]+1.0e0) if (i == 2) return(y[3]) if (i == 3) return(y[4]) if (i == 4) return(y[1]-1-0e0) if (i == 5) return(y[3]) if (i == 6) return(y[4]) } dbceval <- function(i, y, eps,Rpar,Ipar) { if (i == 1) return(c(1, 0,0,0,0,0)) if (i == 2) return(c(0, 0,1,0,0,0)) if (i == 3) return(c(0, 0,0,1,0,0)) if (i == 4) return(c(1, 0,0,0,0,0)) if (i == 5) return(c(0, 0,1,0,0,0)) if (i == 6) return(c(0, 0,0,1,0,0)) } setoutput<- function(neqn,plotsol=NULL){ solref = FALSE 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( ), 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)) }