1550078481-Ordinary_Differential_Equations__Roberts_

CSODE User's Guide 517

" SOLVEIVP S~IE3

SOINEIVP calculates anc;I graphs the solution of>the initial value problem: y'· ~ f(Jt. y); y(c}""' d on the iiilerval (a. li) wheJe a <"' c <"' b

Enter the function f(x. y) = ··'~·"----------­

Enter the interval of iotegrnlion [a. b).

Actual inte1val of integ1ation is (Xmin, Xmax)

Xmin • -1.000000E+OO Xmax • ) 4.000000E•DO Vmin •

Ymax

YminXmin ,__,,~-,:~~.,....~. : • .,...~~~·'-~~~;...-~,,......;.~...,.~""'"~~~•-~~~-'~~~-'-"""'~ Xmmc

Figure A.12 Graph of the Numerical Approximation to the Solution of the

Initial Value Problem y' = x - y; y(O) = 2

on the Interval [ -1, 4]

,. SOLVEIVP li!i00

SOLVElVP calculates and graphs the solution of the initial value problem: y'., f(>c.?); _y(c) • d on the interval [a. b) where a<• c <•bl

Enter the function f(x. y) ,.. x·y

Enter the interval of integration [a. b).

Actual interval of integration is [Xmin, Xmax)

Xmin"" XmaM ... I 4.000000£+00 Ymin • _____ _, Ymax ..^1 ___ ,o_w

Solution Valuea

y(x)

.. _,·9.950000E 1 •. 0.0.oQo.o.E.!OO ·01 ...... 6.119173E oJ.~ 4 ,.845E .. +00! .O.O .. J •

·9.900000E-9.850000£-01 -01 6.083703E+OO 6.048436£+00

·9.BOOOOOE·O·9. 750000£ -01 l 6.5.978502£ 013369E+OO +00

·9.?00000E-01 ·9.650000E·Ol 5.943833£+00 5.909363£+00

·9.GOOOOOE-01 5.875089E+OO

·9.550000E·01 ·9 .500000£-01 5.841012E+OO 5.807129£+00

·9.450000£ -9.400000£ -0-01 1 5. 5. 739944£ 773440£ +00 +00

·9·9.300000£-01 .350000E -01 5. 5.673528£+00 706640E +00

·9·9.200000£ .250000E ·· 01 01 5.5.607871 640605E E +00 +00

·9.150000£-01 ·9.100000£ ·01 5.575326£+00 5.542968£ +00

-9.050000£ ·9.000000£-01 -01 5.510796£ 5.478809£+00 +00

-8·B.900000E·01 .950000£-01 5.447007£+00 5.415389E+OO

·8.850000£·01 5.383953£+00

rngggg~ :81 rnm~t88 EJ

Figure A.13 Solution Values of the IVP y'

on the Interval [-1, 4]

x - y; y(O) 2