C Library Functions - colloc (3)
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from |
* a practical guide to splines * by c. de boor
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Chapter xv, example. solution of an ode by collocation.
calls colpnt, difequ(ppvalu(interv)), knots, eqblok(putit(difequ*,
bsplvd(bsplvb)))), slvblk(various subprograms), bsplpp(bsplvb*),
newnot
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****** |
i n p u t ******
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aleft, aright | | |
endpoints of interval of approximation
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lbegin |
initial number of polynomial pieces in the approximation.
a uniform breakpoint sequence is chosen.
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iorder |
order of polynomial pieces in the approximation
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ntimes |
number of passes through n e w n o t to be made
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addbrk |
the number (possibly fractional) of breaks to be added per
pass through newnot. e.g., if addbrk = .33334, then a break-
point will be added at every third pass through newnot.
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relerr |
a tolerance. newton iteration is stopped if the difference
between the b-coeffs of two successive iterates is no more
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than |
relerr*(absol.largest b-coefficient).
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****** |
p r i n t e d o u t p u t ******
consists of the pp-representation of the approximate solution,
and of the error at selected points.
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****** |
m e t h o d ******
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the m-th order ordinary differential equation with | | |
m side condit-
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ions, to be specified in subroutine | | |
d i f e q u, is solved approx-
imately by collocation.
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the approximation | | |
f to the solution g is pp of order k+m with
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l |
pieces and m-1 continuous derivatives. f is determined by the
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requirement that it satisfy the d.e. at | | |
k points per interval (to
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be specified in | | |
c o l p n t ) and the m side conditions.
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this usually nonlinear system of equations for | | |
f is solved by
newton’s method. the resulting linear system for the b-coeffs of an
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iterate is constructed appropriately in | | |
e q b l o k and then solved
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in |
s l v b l k, a program designed to solve a l m o s t b l o c k
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d i a g o n a l | | |
linear systems efficiently.
there is an opportunity to attempt improvement of the breakpoint
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sequence (both in number and location) through use of | | |
n e w n o t .
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| Nemo Release 3.1 | colloc (3) | June 29, 2025 |
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