Solving Practical Problems Using Difference Equations or Numerical Differentiation
Applying difference equations and numerical differentiation to solve basic practical problems. Experiment 3: Interpolation and Numerical Integration - Problem formulation and solution approaches for interpolation - Principles, advantages, and limitations of Lagrange interpolation - Fundamentals, strengths, and weaknesses of piecewise linear and cubic spline interpolation - MATLAB implementation techniques for piecewise linear and cubic spline interpolation (using functions like interp1 and spline) - Theory and MATLAB coding for trapezoidal and Simpson's integration rules - Error analysis of numerical integration formulas: convergence order concepts - Gaussian quadrature formulas - Generalized integrals and multiple integrals - Applying interpolation and numerical integration to solve real-world problems. Experiment 4: Numerical Solutions of Ordinary Differential Equations - Euler method principles and Runge-Kutta method approaches - Concepts of local truncation error and precision - Runge-Kutta implementations in MATLAB