GATE CE 2017 Set 1 — Question 37
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Engineering Mathematics → Numerical Integration & ODEs → Absolute & Relative Error
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Question
Consider the equation with at . This is numerically solved by using the forward Euler method with a step size, . The absolute error in the solution at the end of the first time step is ___________
Correct answer
7.95 to 8.05
Solution
Given differential equation: with initial condition .Step 1: Find the exact solution.
Integrating both sides:
Using :
So, the exact solution is .
At , the exact value is .Step 2: Find the numerical solution using Forward Euler method.
Formula:
Here , , , and .
.Step 3: Calculate the absolute error.
Absolute Error = .The absolute error is 8.
Integrating both sides:
Using :
So, the exact solution is .
At , the exact value is .Step 2: Find the numerical solution using Forward Euler method.
Formula:
Here , , , and .
.Step 3: Calculate the absolute error.
Absolute Error = .The absolute error is 8.
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