Truncation Error Analysis¶
Contents:
- Truncation Error Analysis
- Overview of truncation error analysis
- Truncation errors in finite difference formulas
- Truncation errors in exponential decay ODE
- Truncation error of the Forward Euler scheme
- Truncation error of the Crank-Nicolson scheme
- Truncation error of the \(\theta\)-rule
- Using symbolic software
- Empirical verification of the truncation error
- Increasing the accuracy by adding correction terms
- Extension to variable coefficients (1)
- Exact solutions of the finite difference equations
- Computing truncation errors in nonlinear problems
- Truncation errors in vibration ODEs
- Truncation errors in wave equations
- Truncation errors in diffusion equations
- Exercises
- Exercise 1: Truncation error of a weighted mean
- Exercise 2: Simulate the error of a weighted mean
- Exercise 3: Verify a truncation error formula
- Exercise 4: Truncation error of the Backward Euler scheme
- Exercise 5: Empirical estimation of truncation errors
- Exercise 6: Correction term for a Backward Euler scheme
- Exercise 7: Verify the effect of correction terms
- Exercise 8: Truncation error of the Crank-Nicolson scheme
- Exercise 9: Truncation error of \(u'=f(u,t)\)
- Exercise 10: Truncation error of \([D_t D_tu]^n\)
- Exercise 11: Investigate the impact of approximating \(u'(0)\)
- Exercise 12: Investigate the accuracy of a simplified scheme
