# MTH603 Quiz 3 Solution and Discussion

• Euler’s Method numerically computes the approximate ________ of a function.

• Given that dydt=t+y√dydt=t+y with the initial condition y0=1att0=0y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1.

Solution Web

• Given that dydt=t+y√dydt=t+y with the initial condition y0=1att0=0y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1.

• Given that dydt=y−ty+tdydt=y−ty+t with the initial condition y=1,t=0y=1,t=0 find the 3rd term in Taylor series when t=0.3 and y//= 0.2.

Solution

• Given that dydt=y−ty+tdydt=y−ty+t with the initial condition y=1,t=0y=1,t=0 find the 3rd term in Taylor series when t=0.3 and y//= 0.2.

• In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.

R.K Methods do not require prior calculation of higher derivatives of y(x) ,as the Taylor method does. Since the differential equations using in applications are often complicated, the calculation of derivatives may be difficult

• In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.

• Multistep method does not improves the accuracy of the answer at each step.

Multistep methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Consequently, multistep methods refer to several previous points and derivative values.

• Multistep method does not improves the accuracy of the answer at each step.

• If yn+1=yn+16(K1+2K2+2k3+k4)yn+1=yn+16(K1+2K2+2k3+k4) then, K2K2 is:

• Given that dydt=t+y√dydt=t+y with the initial condition y0=1att0=0y0=1att0=0 Using Modified Euler’s method, for the range 0⩽t⩽0.60⩽t⩽0.6, h = 0.1 is

• Euler’s method is only useful for a few steps and small step sizes; however Euler’s method together with Richardson extrapolation may be used to increase the ____________.

Order accuracy is the percentage of all ecommerce orders that are fulfilled and shipped to their final destination without error, such as a mis-pick of an item or incorrect unit quantity. Order accuracy is an important metric to track because it highly impacts customer satisfaction.

• Euler’s method is only useful for a few steps and small step sizes; however Euler’s method together with Richardson extrapolation may be used to increase the ____________.

• Given that dydt=y−ty+tdydt=y−ty+t with the initial condition y=1.01 at t=0.01. Using Euler’s method, y at t= 0.04, h=0.05, the value of y(0.05) is

• Generally, Adams methods are superior of output at many points is needed.

The Adams methods are useful to reduce the number of function calls, but they usually require more CPU time than the Runge-Kutta methods.

• Generally, Adams methods are superior of output at many points is needed.

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