MATLAB 5.0 MAT-file, Platform: PCWIN, Created on: Sat Nov 26 23:00:53 2005 IM - hgS_070000 7typehandlepropertieschildrenspecial@ figure8 i@0!UnitsColorColormapFileNameIntegerHandleInvertHardcopyMenuBarNameNumberTitlePaperPositionPositionResizeHandleVisibilityTagUserDataApplicationDataBehaviorH characters00@ ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????7nC:\MFILES.KEA\Guide_Dir\Guide_NA.dir\Euler_ODE_Help.fig8off0on8nonePEuler_ODE_Help8offP ?@ @@02t78off@callback@figure108 GUIDEOptionslastValidTagactive_htaginfooverridereleaseresizeaccessibilitymfilecallbackssingletonsyscolorfigblockinglastSavedFile0figuretext0000 8none@callback000005jC:\MFILES.KEA\Guide_Dir\Guide_NA.dir\Euler_ODE_Help.m@figure18 7typehandlepropertieschildrenspecialH uicontrol8 i@UnitsBackgroundColorFontSizePositionStringStyleTagApplicationDataBehaviorH characters00P 3@I@̌Q@NN@`,HELP FOR EULER_ODE_GUI8text@ text1  lastValidTag@ text18H uicontrol8 >@hUnitsBackgroundColorFontSizeHorizontalAlignmentPositionStringStyleTagApplicationDataBehaviorH characters00 8leftP #@ON@ Y@ى؉G@ %JThis solves the initial value problemP y = f(x,y)Pon the interval [0,b] with y(0)=Y0 given. The actual problems being solved are *Tas follows, along with the true solutions.07n1. y = c y + (d-c) cos(d x) - (d+c) sin(d x), y(0)=10` True solution: Y(x) = sin (d x) + cos (d x)`,2. y = c y, y(0)=1.x#F True solution: Y(x) = exp(c x)&L3. y = (y + x^2 -2)/(x+1), y(0) = 2:t True solution: Y(x) = x^2 + 2*x +2 - 2*(x+1) log(x+1)(P4. y = c y + (d-c) exp(d x), y(0) = 1x#F True solution: Y(x) = exp(d x)h85. y = cos(y)^2, y(0) = 0x"D True solution: Y(x) = atan(x)h26. y = c y^2, y(0) = 1&L True solution: Y(x) = 1/(1 - c x)p>7. y = c y (d y), y(0) = 1F True solution: Y(x) = d{1 [1 + exp(c d x)/(d-1)]^(-1)}, d ~= 00JThe parameters c and d can be given in the appropriate text windows. The Nsolution is calculated for the given stepsize h and also for a stepsize of 2h.0IThe true errors are also given in both cases. The print parameter means .\that the solutions will be given at the pointsh8 x = 0,2Mh,4Mh,6Mh,. . .0BThe Richardson error estimate for a numerical method of order 1 is<x Y(x) y_h(x) approximately equals y_h(x) y_2h(x)LWhether this is accurate or not can be checked by the student in particular Kcases. In doing so, consider the same problem with decreasing values of h.08text@ text2  lastValidTag@ text28