Program For Bisection Method In Fortran 95
Simple programs
# Quadratic equation ax^2 + bx + c = 0
# Fibonacci numbers
# Legendre polynomials Pn(x)
C Programming - Program for Bisection Method - Mathematical Algorithms - The method is also called the interval halving method, the binary search method Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’ such that f(a).f(b). BISECTION_RC is a FORTRAN90 library which demonstrates the simple bisection method for solving a scalar nonlinear equation in a change of sign interval, using reverse communication (RC). Reverse communication instead allows the user's calling program to retain control of the function evaluation.
Program For Bisection Method In Fortran 95 Tutorial
Real roots of non-linear equations
# Bisectional method Bisection.f90
# Closed Domain (Bisectional or False position selected by a key) CDomain.f90
# Open Domain: Newton's method Newton1.f90
# Open Domain: The method of secants Secant.f90
# Brute force method for multiple roots BForce.f90
# Solutions of a system of two nonlinear equations f(x,y) = 0, g(x,y) = 0 Newton2.f90
Integration of a single variable function f(x)
# Simpson rule on n intervals (simpson.f90)
# Integration based based on Gauss 8 points or 16 points (gauss.f90)
# Automatic adaptive integration based on Simpson rule (simpson2.f90)
# Automatic adaptive integration based on Gauss quaratures (gauss2.f90)
# Automatic adaptive integration - Gauss quaratures + recursive calls (gaussA.f90)
# Trapezoid approximation for n intervals (int_trap.f)
# Automatic adaprive integration - Newton-Cotes quadrature (program quanc8.f)
# Driver program for int_trap.f, quanc8.f
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Integration of a function of two variables f(x,y)
# Integration of a function f(x,y) using cubature trapezoid rule (trap_2Dc.f90)
# Automatic adaptive Integration of a function f(x,y) using Simpson rule (simpson2D.f90)
Interpolation (single variable)
# Polinomial (Lagrange) interpolation Lagint.f90
# Polinomial (Divided differences) interpolation DDint.f90
# Spline interpolation Spline.f90
| Chapter 1: Introduction | ||
| first.f90 | 6-7 | First programming experiment |
| pi.f90 | 8 | Simple code to illustrate double precision |
| Chapter 2: Number Representation and Errors | ||
| oct.f90 | 49 | Print in octal format |
| hex.f90 | 50 | Print in hexadecimal format |
| numbers.f90 | 60-61 | Print internal machine representation of various numbers |
| xsinx.f90 | 77-79 | Example of carefully programming f(x) = x - sinx |
| Chapter 3: Locating Roots of Equations | ||
| bisection.f90 | 94-95 | Bisection method |
| rec_bisection.f90 | 95-96 | Recursive version of bisection method |
| newton.f90 | 106-107 | Sample Newton method |
| secant.f90 | 127-128 | Secant method |
| Chapter 4: Interpolation and Numerical Differentiation | ||
| coef.f90 | 152-155 | Newton interpolation polynomial at equidistant pts |
| deriv.f90 | 185-186 | Derivative by center differences/Richardson extrapolation |
| Chapter 5: Numerical Integration | ||
| sums.f90 | 200 | Upper/lower sums experiment for an integral |
| trapezoid.f90 | 207 | Trapezoid rule experiment for an integral |
| romberg.f90 | 223-224 | Romberg arrays for three separate functions |
| Chapter 6: More on Numerical Integration | ||
| rec_simpson.f90 | 241 | Adaptive scheme for Simpson's rule |
| Chapter 7: Systems of Linear Equations | ||
| ngauss.f90 | 270-271 | Naive Gaussian elimination to solve linear systems |
| gauss.f90 | 285-287 | Gaussian elimination with scaled partial pivoting |
| tri.f90 | 301-302 | Solves tridiagonal systems |
| penta.f90 | 304 | Solves pentadiagonal linear systems |
| Chapter 8: More on Systems of Linear Equations | ||
| Chapter 9: Approximation by Spline Functions | ||
| spline1.f90 | 385 | Interpolates table using a first-degree spline function |
| spline3.f90 | 404-406 | Natural cubic spline function at equidistant points |
| bspline2.f90 | 427-428 | Interpolates table using a quadratic B-spline function |
| schoenberg.f90 | 430-431 | Interpolates table using Schoenberg's process |
| Chapter 10: Ordinary Differential Equations | ||
| euler.f90 | 448-449 | Euler's method for solving an ODE |
| taylor.f90 | 451 | Taylor series method (order 4) for solving an ODE |
| rk4.f90 | 462-463 | Runge-Kutta method (order 4) for solving an IVP |
| rk45.f90 | 472-473 | Runge-Kutta-Fehlberg method for solving an IVP |
| rk45ad.f90 | 474 | Adaptive Runge-Kutta-Fehlberg method |
| Chapter 11: Systems of Ordinary Differential Equations | ||
| taylorsys1.f90 | 489-490 | Taylor series method (order 4) for systems of ODEs |
| taylorsys2.f90 | 491 | Taylor series method (order 4) for systems of ODEs |
| rk4sys.f90 | 491-493,496 | Runge-Kutta method (order 4) for systems of ODEs |
| amrk.f90 | 510-513 | Adams-Moulton method for systems of ODEs |
| amrkad.f90 | 513 | Adaptive Adams-Moulton method for systems of ODEs |
| Chapter 12: Smoothing of Data and the Method of Least Squares | ||
| Chapter 13: Monte Carlo Methods and Simulation | ||
| test_random.f90 | 562-563 | Example to compute, store, and print random numbers |
| coarse_check.f90 | 564 | Coarse check on the random-number generator |
| double_integral.f90 | 574-575 | Volume of a complicated 3D region by Monte Carlo |
| volume_region.f90 | 575-576 | Numerical value of integral over a 2D disk by Monte Carlo |
| cone.f90 | 576-577 | Ice cream cone example |
| loaded_die.f90 | 581 | Loaded die problem simulation |
| birthday.f90 | 583 | Birthday problem simulation |
| needle.f90 | 584 | Buffon's needle problem simulation |
| two_die.f90 | 585 | Two dice problem simulation |
| shielding.f90 | 586-587 | Neutron shielding problem simulation |
| Chapter 14: Boundary Value Problems for Ordinary Differential Equations | ||
| bvp1.f90 | 602-603 | Boundary value problem solved by discretization technique |
| bvp2.f90 | 605-606 | Boundary value problem solved by shooting method |
| Chapter 15: Partial Differential Equations | ||
| parabolic1.f90 | 618-619 | Parabolic partial differential equation problem |
| parabolic2.f90 | 620-621 | Parabolic PDE problem solved by Crank-Nicolson method |
| hyperbolic.f90 | 633-634 | Hyperbolic PDE problem solved by discretization |
| seidel.f90 | 642-645 | Elliptic PDE solved by discretization/ Gauss-Seidel method |
| Chapter 16: Minimization of Functions | ||
| Chapter 17: Linear Programming | ||
Addditional programs can be found at the textbook's anonymous ftp site:
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