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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 0sx<1 | Hence, if the exact solution is y = 2eT –1, find its errors.

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 0sx<1 | Hence, if the exact solution is y = 2eT –1, find its errors.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 Taylor's series method with h = 0.1,0.25,0.5 and 0<xs1 | | Hence, if the exact solution is y = 2e -1, find its errors. Answer : (b) h=0.1 Jerror| exact 1.000 1.010 1.040 1.091 1.000 1.010 1.040 1.092 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 9 0.000 0.000 0.001 0.002 0.002 0.003 0.004 0.005 0.008 0.010 1.165 1.264 1.391 1.167 1.266 1.551 1.749 1.991 2.287 1.394 1.555 1.754 1.999 2.297 0.9 10 1.0 h-0.25 erro| exact 1.000 1.000 0.25 0.50 3 1 1.062 1.259 1.629 1.063 1.266 1.650 2.297 0.001 0.007 0.021 0.75 4 1.00 2.249 0.048 h-0.5 Jerrot| exact 0.5 1.0 1.000 1.250 2.164 1.000 1.266 2.297 0.016 0.133
Transcribed Image 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<xs1 | | Hence, if the exact solution is y = 2e -1, find its errors. Answer : (b) h=0.1 Jerror| exact 1.000 1.010 1.040 1.091 1.000 1.010 1.040 1.092 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 9 0.000 0.000 0.001 0.002 0.002 0.003 0.004 0.005 0.008 0.010 1.165 1.264 1.391 1.167 1.266 1.551 1.749 1.991 2.287 1.394 1.555 1.754 1.999 2.297 0.9 10 1.0 h-0.25 erro| exact 1.000 1.000 0.25 0.50 3 1 1.062 1.259 1.629 1.063 1.266 1.650 2.297 0.001 0.007 0.021 0.75 4 1.00 2.249 0.048 h-0.5 Jerrot| exact 0.5 1.0 1.000 1.250 2.164 1.000 1.266 2.297 0.016 0.133
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!
Transcribed Image 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!
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