Get expert advice and community support for your questions on IDNLearn.com. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.
The centered difference discretization method can easily be constructed for higher order approximation. Construct the 4ᵗʰ-order accurate centered difference discrete equation. Here are the hints: Start with the Taylor's expansion for f(x + Δx): f(x + Δx) ≈ f(x) + df/dx Δx + d²f/dx² Δx² / 2 + d³f/dx³ Δx³ / 6 + d⁴f/dx⁴ Δx⁴ / 24 + o(Δx⁵) f(x - Δx) ≈ f(x) - df/dx Δx + d²f/dx² Δx² / 2 - d³f/dx³ Δx³ / 6 + d⁴f/dx⁴ Δx⁴ / 24 + o(Δx⁵) 1. Expand for f(x + -2Δx). 2. Calculate f(x + Δx) - f(x - Δx). 3. Calculate f(x + 2Δx) - f(x - 2Δx). 4. Compare (3) and (4). Remove the unnecessary terms.
Sagot :
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.
