Practice Fundamental Concepts - 18.1 | 18. Stability and Convergence of Methods | Mathematics - iii (Differential Calculus) - Vol 4
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Fundamental Concepts

18.1 - Fundamental Concepts

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Practice Questions

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Question 1 Easy

Define an Ordinary Differential Equation.

💡 Hint: Focus on the function and derivatives.

Question 2 Easy

What is a numerical method?

💡 Hint: Think about how we use methods to calculate values.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the definition of an Ordinary Differential Equation (ODE)?

A type of algebraic equation
An equation involving functions and their derivatives
A polynomial equation

💡 Hint: Think about the components of an ODE.

Question 2

True or False: Stability ensures that errors grow uncontrollably.

True
False

💡 Hint: Remember the definition of stability.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the ODE y' = -3y with initial condition y(0) = 2, apply Euler’s method with a step size of 0.5 to find the approximation at x = 1.

💡 Hint: Pay attention to how you apply the recurrence relation.

Challenge 2 Hard

Analyze the convergence of the numerical solution for the ODE y' = -y as h approaches zero, discussing the impact on accuracy.

💡 Hint: Consider what happens as you make step sizes smaller.

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