GATE ME 2014 Set 4 — Question 39
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Engineering Mathematics → Numerical Methods → Euler & Runge-Kutta Methods
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Question
Consider an ordinary differential equation . If at , the increment in calculated using Runge-Kutta fourth order multi-step method with a step size of is
Correct answer
(D) 0.88
Solution
The given differential equation is .
Since is a function of only, the increment in over a step is exactly the integral of over that interval.
Runge-Kutta 4th order method is equivalent to Simpson's 1/3 rule for integration when the function depends only on the independent variable. RK4 is exact for polynomials up to degree 3. Since is a linear polynomial (degree 1), the RK4 result will be exact.
Increment
.
Since is a function of only, the increment in over a step is exactly the integral of over that interval.
Runge-Kutta 4th order method is equivalent to Simpson's 1/3 rule for integration when the function depends only on the independent variable. RK4 is exact for polynomials up to degree 3. Since is a linear polynomial (degree 1), the RK4 result will be exact.
Increment
.
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