MA8459-NUMERICAL METHODS UNIT - IV QUIZ

Euler corrector is ________.

• Yn+1 =Yn+hYn.
• Y n+1 = Yn+h/2(Yn + Y n+1)
• Y n+1 = Yn +h/2(Y'n+Y' n+1)
• Y n+1 = Yn' -hYn'

In Euler's method: Given initial value problem y'=dy/dx=f(x, y) with y(x0) = y0, then approximation is given by ________.

• yn+1=yn+hf(xn-1, yn-1)
• yn+1=yn+hf(xn, yn)
• yn+1=yn+hf(xn-1, yn)
• yn+1=yn+hf(xn, yn-1)

y(x+h) = y(x) + h f(x,y) is referred as __________ method.

• Euler
• Modified Euler
• Taylor's Series
• Runge-Kutta

The order of Euler method is __________.

• h
• h^ 2
• h^3
• h^ 4

Taylor's series method will be very useful to give some initial starting values for powerful methods such as _______.

• Euler Method
• Modified Euler Method
• Newton Raphson Method
• Runge Kutta Method

The modified Euler method is based on the average of ________.

• straight line
• ellipse
• chord
• points

The simplest method in finding the approximate solutions to the first order equations is _______.

• Euler's method
• Modified Euler's Method
• Runge-Kutta method
• Taylor's Method

The most popular Runge-Kutta method is ______.

• First order Runge-Kutta method
• Second order Runge-Kutta method
• Third order Runge-Kutta method
• Fourth order Runge-Kutta method

In the two-level predictor-corrector method, the prediction is done using _____________

• trapezoidal rule
• explicit Euler method
• midpoint rule
• implicit Euler method

The two-level predictor-corrector method is __________

• second-order accurate
• first-order accurate
• fourth-order accurate
• third-order accurate