COMPUTER-ORIENTED NUMERICAL METHODSNumerical methods are powerful problem-solving tools. Techniques of these methods are capable of handling large systems of equations, nonlinearities and complicated geometries in engineering practice which are impossible to be solved analytically. Numerical methods can solve the real world problem using the C program given in this book. This well-written text explores the basic concepts of numerical methods and gives computational algorithms, flow charts and programs for solving nonlinear algebraic equations, linear equations, curve fitting, integration, differentiation and differential equations. The book is intended for students of B.E. and B.Tech as well as for students of B.Sc. (Mathematics and Physics). KEY FEATURES Gives clear and precise exposition of modern numerical methods. Provides mathematical derivation for each method to build the student’s understanding of numerical analysis. Presents C programs for each method to help students to implement the method in a programming language. Includes several solved examples to illustrate the concepts. Contains exercises with answers for practice. |
Contents
1 | |
Chp1a | 20 |
Chp1b | 47 |
Chp1c | 65 |
Chp2 | 97 |
Chp2a | 127 |
Chp3 | 165 |
Chp4 | 188 |
Chp5a | 327 |
Chp5b | 351 |
Chp5c | 374 |
Chp6 | 404 |
Chp7 | 421 |
Chp7a | 448 |
Chp7b | 477 |
Chp7c | 500 |
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A²y_1 A²yo A³y_1 A³yo ALGORITHM approximation augmented matrix bisection method central difference clrscr coefficients compute decimal places difference equation difference formula difference table differential equation divided difference dx² dy dx Ë Ì Ì eigenvalues eigenvectors End loop Enter the value Euler's method Evaluate EXAMPLE f(xo find the value FLOW CHART forward formula function Gauss getch given Hence hf(x Ì Ì Ì include conio.h include math.h initial values integral interpolation formula interval ITERATION METHOD k₁ Lagrange's Milne's Ñ Ñ Newton-Raphson Method Newton's forward numerical polynomial positive root printf Enter PROGRAM include stdio.h root lies Runge-Kutta method secant method Simpson's rule Solution Let Taylor series trapezoidal rule Ü Ü Ü Ü Ü Ý Void main x₁ y₁ Yn+1 хо