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: real scalar or vector. Gives instants for which you want the solution. Note that you can get solution at each dassl's step point by setting \fVinfo(2)=1\fR.

.TP

: a vector with two entries \fV[times num]\fR \fVtimes\fR is the value

of the time at which the surface is crossed, \fVnum\fR is the number

of the crossed surface

.TP

atol,rtol

: real scalars or column vectors of same size as \fVy\fR. \fVatol,rtol\fR give respectively absolute and relative error tolerances of solution.

If vectors the tolerances are specified for each component of \fVy\fR.

.TP

res

: external (function or list or string). Computes the value of \fVg(t,y,ydot)\fR.

.RS

.TP 8

function

: Its calling sequence must be \fV[r,ires]=res(t,y,ydot)\fR

and \fVres\fR must return the residue \fVr=g(t,y,ydot)\fR and error flag

\fVires\fR. \fVires = 0\fR if \fVres\fR succeeds to compute \fVr\fR, \fV=-1\fR

if residue is locally not defined for \fV(t,y,ydot)\fR, \fV=-2\fR if

parameters are out of admissible range.

.TP

list

: it must be as follows:

.nf

list(res,x1,x2,...)

.fi

where the calling sequence of the function \fVres\fR is now

.nf

r=res(t,y,ydot,x1,x2,...)

.fi

\fVres\fR still returns \fVr=g(t,y,ydot)\fR as a function of

\fV(t,y,ydot,x1,x2,...)\fR.

.TP

string

: it must refer to the name of

a fortran subroutine (see source code of \fVfresd.f\fR).

.RE

.TP

jac

: external (function or list or string). Computes the value

of \fVdg/dy+cj*dg/dydot\fR for a given value of parameter \fVcj\fR

.RS

.TP 8

function

: Its calling sequence must be \fVr=jac(t,y,ydot,cj)\fR

and the \fVjac\fR function must return

\fVr=dg(t,y,ydot)/dy+cj*dg(t,y,ydot)/dydot\fR where \fVcj\fR is a real scalar

.TP

list

: it must be as follows

.nf

list(jac,x1,x2,...)

.fi

where the calling sequence of the function \fVjac\fR is now

.nf

r=jac(t,y,ydot,x1,x2,...)

.fi

\fVjac\fR still returns \fVdg/dy+cj*dg/dydot\fR as a function of

\fV(t,y,ydot,cj,x1,x2,...)\fR.

.TP

character string

: it must refer to the name of a fortran subroutine

(see source code of \fVjacdd.f\fR).

.RE

.TP

surf

: external (function or list or string). Computes the value

of the column vector \fVsurf(t,y)\fR with ng components.

Each component defines a surface.

.RS

100

.TP 8

101

function

102

: Its calling sequence must be \fVsurf(t,y)\fR

103

.TP

104

list

105

: it must be as follows

106

.nf

107

list(surf,x1,x2,...)

108

.fi

109

where the calling sequence of the function \fVsurf\fR is now

110

.nf

111

r=surf(t,y,x1,x2,...)

112

.fi

113

.TP

114

character string

115

: it must refer to the name of a fortran subroutine

116

(see source code of \fVfsurfd.f\fR) in directory \fVSCDIR/default\fR

117

.RE

118

.TP

119

info

120

: list which contains \fV7\fR elements, default value is list([],0,[],[],[],0,0)

121

.RS

122

.TP 8

123

info(1)

124

: real scalar which gives the maximum time for which \fVg\fR is allowed

125

to be evaluated or an empty matrix \fV[]\fR if no limits imposed for time.

126

.TP

127

info(2)

128

: flag which indicates if \fVdassl\fR returns its intermediate

129

computed values (\fVflag=1\fR) or only the user specified time point

130

values (\fVflag=0\fR).

131

.TP

132

info(3)

133

: \fV2\fR components vector which give the definition \fV[ml,mu]\fR of band

134

matrix computed by \fVjac\fR;

135

\fVr(i - j + ml + mu + 1,j) = "dg(i)/dy(j)+cj*dg(i)/dydot(j)"\fR.

136

If \fVjac\fR returns a full matrix set \fVinfo(3)=[]\fR.

137

.TP

138

info(4)

139

: real scalar which gives the maximum step size. Set \fVinfo(4)=[]\fR if no

140

limitation.

141

.TP

142

info(5)

143

: real scalar which gives the initial step size. Set \fVinfo(4)=[]\fR if

144

not specified.

145

.TP

146

info(6)

147

: set \fVinfo(6)=1\fR if the solution is known to be non negative,

148

else set \fVinfo(6)=0\fR.

149

.TP

150

info(7)

151

: set \fVinfo(7)=1\fR if \fVydot0\fR is just an estimation, \fVinfo(7)=0\fR

152

if \fVg(t0,y0,ydot0)=0\fR.

153

.RE

154

.TP

155

156

: real vector which allows to store the \fVdassl\fR context and to

157

resume integration

158

.TP

159

160

: real matrix . Each column is the vector [t;x(t);xdot(t)] where t is time

161

index for which the solution had been computed

162

.SH DESCRIPTION

163

Solution of the implicit differential equation

164

.nf

165

g(t,y,ydot)=0

166

y(t0)=y0 and ydot(t0)=ydot0

167

.fi

168

Returns the surface crossing instants and the number of the

169

surface reached in \fVnn\fR.

170

171

Detailed examples can be found in SCIDIR/tests/dassldasrt.tst

172

.SH EXAMPLE

173

.nf

174

//dy/dt = ((2*log(y)+8)/t -5)*y, y(1) = 1, 1<=t<=6

175

//g1 = ((2*log(y)+8)/t - 5)*y

176

//g2 = log(y) - 2.2491

177

y0=1;t=2:6;t0=1;y0d=3;

178

atol=1.d-6;rtol=0;ng=2;

179

180

deff('[delta,ires]=res1(t,y,ydot)','ires=0;delta=ydot-((2*log(y)+8)/t-5)*y')

181

deff('[rts]=gr1(t,y)','rts=[((2*log(y)+8)/t-5)*y;log(y)-2.2491]')

182

183

[yy,nn]=dasrt([y0,y0d],t0,t,atol,rtol,res1,ng,gr1);

184

//(Should return nn=[2.4698972 2])

185

.fi

186

.SH SEE ALSO

187

ode, dassl, impl, fort, link, external

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