Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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4. Taylor method of order three is given by h Yi+1 = Y¡ + hT (³) (t₁, Y;), where T(³) (t¡‚, Y;) = ƒ (t¡‚Y;) + − ƒ' (t¡‚Y;) + h² - ƒ"(ti, Y;) 3! Write out this method's formula when it is applied to the IVP: y' = -y + sin t. (The formula expression should have no f, f', or f", it should only involves t, h and y. Do not carry out the actual calculations)
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Transcribed Image Text:4. Taylor method of order three is given by h Yi+1 = Y¡ + hT (³) (t₁, Y;), where T(³) (t¡‚, Y;) = ƒ (t¡‚Y;) + − ƒ' (t¡‚Y;) + h² - ƒ"(ti, Y;) 3! Write out this method's formula when it is applied to the IVP: y' = -y + sin t. (The formula expression should have no f, f', or f", it should only involves t, h and y. Do not carry out the actual calculations)
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