A textbook of Computer Based Numerical and Statiscal Techniques part 2. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | CONTENTS . Relation Between Divided Differences and Ordinary Differences 247 Newton s Divided Difference Formula 247 Problem Set 258 . Hermite s Interpolation Formula 259 Problem Set 261 . Some Related Terms 269 Some Remarkable Points about Chosen Different Interpolation Formulae 269 Approximation of Function 270 Spline Interpolation 285 Cubic Spline Interpolation for Equally and Unequally Spaced Values 286 Problem Set 291 6. Numerical Differentiation and Integration 294-331 Introduction 294 Numerical Differentiation 294 Derivation Using Newton s Forward Interpolation Formula 295 Derivatives Using Newton s Backward Difference Formula 296 Derivatives Using Stirling s Formula 298 Derivative Using Newton s Divided Difference Formula 298 Problem Set 313 Numerical Integration 315 General Quadrature Formula 315 Trapezoidal Rule 316 Simpson s One-Third Rule 316 Simpson s Three-Eight Rule 317 Boole s Rule 317 Weddle s Rule 318 Euler-Maclaurin s Formula 327 Problem Set 330 7. Numerical Solution of Ordinary Differential Equation 332-372 Introduction 332 Taylor s Method 332 Picard s Method of Successive Approximations 336 Euler s Method 342 Euler s Modified Method 343 Problem Set 351 Runge-Kutta Method 352 Milne s Predictor-Corrector Method 361 Predictor-Corrector Methods 361 Milne s Method 361 CONTENTS Automatic Error Monitoring 369 Convergence of a Method 370 Stability in the Solution of Ordinary Differential Equation 370 Problem Set 372 8. Solution of Simultaneous Linear Equation Introduction 373 Gauss-Elimination Method 373 Gauss-Elimination with Pivoting Method 375 Ill-Conditioned System of Equations 376 Iterative Refinement of the Solution by Gauss Elimination Method 376 Iterative Method for Solution of Simultaneous Linear Equation 377 Jacobi s Method or Gauss-Jacobi Method .
