P. 592, lines 11 and 12: Difference between revisions

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<math>x(t + \Delta t) \approx x(t) + \frac{\Delta t}{2} \left[ \left(-x^3(t) + \sin \left(t x(t) \right) \right) + \left( -\left(x(t) + f(x(t),t) \Delta t \right)^3 + \sin \left( (t + \Delta t)(x(t) + f(x(t),t) \Delta t) \right)  \right)\right]</math>
<math>x(t + \Delta t) \approx x(t) + \frac{\Delta t}{2} \left[ \left(-x^3(t) + \sin \left(t x(t) \right) \right) + \left( -\left(x(t) + f(x(t),t) \Delta t \right)^3 + \sin \left( (t + \Delta t)(x(t) + f(x(t),t) \Delta t) \right)  \right)\right]</math>
<math>\qquad = x(t) + \frac{\Delta t}{2} \left[ \left(-x^3(t) + \sin \left(t x(t) \right) \right) + \left( -\left(x(t) + (-x^3(t) + \sin(t x(t))) \Delta t \right)^3 + \sin \left( (t + \Delta t)(x(t) + (-x^3(t) + \sin(t x(t))) \Delta t) \right)  \right)\right]</math>


[[Engineering Differential Equations: Theory and Applications, Springer 2010#Errata|Return to errata.]]
[[Engineering Differential Equations: Theory and Applications, Springer 2010#Errata|Return to errata.]]

Latest revision as of 15:13, 18 December 2012

The equation should be

x(t+Δt)≈x(t)+Δt2[(−x3(t)+sin⁡(tx(t)))+(−(x(t)+f(x(t),t)Δt)3+sin⁡((t+Δt)(x(t)+f(x(t),t)Δt)))]

=x(t)+Δt2[(−x3(t)+sin⁡(tx(t)))+(−(x(t)+(−x3(t)+sin⁡(tx(t)))Δt)3+sin⁡((t+Δt)(x(t)+(−x3(t)+sin⁡(tx(t)))Δt)))]

Return to errata.

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