15 - Numerical Solutions of ODEs
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What does the acronym IVP stand for?
💡 Hint: Think about how we begin solving differential equations.
What is meant by step size in numerical methods?
💡 Hint: It's related to how quickly we move along the x-axis.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What type of method is the Adams-Bashforth method?
💡 Hint: Recall the key features of Adams-Bashforth.
True or False: The Local Truncation Error for a 2-step Adams-Bashforth method is O(h^2).
💡 Hint: Consider the definition of Local Truncation Error.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given the ODE $\frac{dy}{dx} = y + 3x^2$ with initial condition $y(0)=1$, apply the 4-step Adams-Bashforth method to compute an approximation to $y(0.6)$ using a step size of $h=0.2$. Start with values obtained from a single-step method.
💡 Hint: Don’t forget to derive initial values before applying the 4-step method.
Critically analyze how increasing the number of steps in the Adams-Bashforth method affects accuracy and computational load. Provide a practical scenario where one might choose a higher or lower step count.
💡 Hint: Reflect on typical use-cases for rapid versus precise results.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.