By using second order Taylor's series method formula solve the ordinary differentation equation. 5. Solve the following initial value problem (IVP) y' - xy = x; v(0) = 1 by using (b) second-order...



By usingsecond order Taylor's series method formula solve the ordinary differentation equation.



5. Solve the following initial value problem (IVP)<br>y' - xy = x; v(0) = 1<br>by using<br>(b) second-order Taylor's series method with h = 0.1,0.25,0.5 and 0<xs1<br>|<br>| Hence, if the exact solution is y = 2e -1, find its errors.<br>Answer :<br>(b) h=0.1<br>Jerror|<br>exact<br>1.000<br>1.010<br>1.040<br>1.091<br>1.000<br>1.010<br>1.040<br>1.092<br>0.1<br>0.2<br>0.3<br>0.4<br>0.5<br>0.6<br>0.7<br>0.8<br>9<br>0.000<br>0.000<br>0.001<br>0.002<br>0.002<br>0.003<br>0.004<br>0.005<br>0.008<br>0.010<br>1.165<br>1.264<br>1.391<br>1.167<br>1.266<br>1.551<br>1.749<br>1.991<br>2.287<br>1.394<br>1.555<br>1.754<br>1.999<br>2.297<br>0.9<br>10 1.0<br>h-0.25<br>erro|<br>exact<br>1.000<br>1.000<br>0.25<br>0.50<br>3<br>1<br>1.062<br>1.259<br>1.629<br>1.063<br>1.266<br>1.650<br>2.297<br>0.001<br>0.007<br>0.021<br>0.75<br>4<br>1.00<br>2.249<br>0.048<br>h-0.5<br>Jerrot|<br>exact<br>0.5<br>1.0<br>1.000<br>1.250<br>2.164<br>1.000<br>1.266<br>2.297<br>0.016<br>0.133<br>

Extracted text: 5. Solve the following initial value problem (IVP) y' - xy = x; v(0) = 1 by using (b) second-order Taylor's series method with h = 0.1,0.25,0.5 and 0
Formula<br>Second Order Taylor Series Method<br>y(x) = y(x;) + hy'(x;) +

Extracted text: Formula Second Order Taylor Series Method y(x) = y(x;) + hy'(x;) + "(x,) When the Taylor's series is truncated after three terms, it is called second order Taylor's series method. Else, we write as Vis = y; + hy + 2!

Jun 04, 2022
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