I'm trying to implement Bisection Method with Fortran 90 to get solution, accurate to within 10^-5 for 3x - e^x = 0 for 1. Edius pro 9 download free. The bisection method is simple, robust, and straight-forward: take an interval a, b such that f(a) and f(b) have opposite signs, find the midpoint of a, b, and then decide whether the root lies on a, (a+ b)/2 or (a+ b)/2, b. Repeat until the interval is. Write a Fortran program to find first derivation of the.: Orthogonal polynomials generator. The most basic problem in Numerical Analysis (methods) is the root-finding problem. The Bisection Method is a simple root finding method, easy to implement and very robust. The disadvantages of this method. Program For Bisection Method In Fortran Download January 21 2019 The bisection method in mathematics is a root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further.
In the following table, each line/entry contains the program file name, the page number where it can be found in the textbook, and a brief description. Click on the program name to display the source code, which can be downloaded.| 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: V torrent.
| [Home] | [Features] | [TOC] | [Purchase] | [Sample Code] | [Web] | [Manuals] | [Errata] | [Links] |
| Last updated: 5/20/2003 |
Fortran Program For Bisection Method
which says that if a continuous function changes sign over an interval, there is at least one root of the function in that interval. Here is how to find a root using this method.
- Assign end points for the 'root hunt'. Let's call them 'a' ad 'b'. The end points should be such that the value of the function, f at both points should be opposite in sign.i.e. f(a), f(b)<0. This is because we will search for a point within this limit that has zero value for the function or a point where the function crosses the x-axis of the Cartesian Plane. If the end points have the same sign, we can use the GO TO statement to read new values for a and b.
- We choose the mid-point of this interval. Now this mid-point, let's call it 'c', will have some value for the function, namely f(c). Evidently, f(c) will have a positive or negative sign unless it has the value zero in which case it is the root.
- If f(c) has a sign opposite to f(a) or f(b), we will continue searching the root between f(c) and that particular endpoint. Obviously, it cannot have a sign opposite to both as per our choice of a and b. Depending on which end has the opposite sign, either a will take the value of c or c will take the value of b.
- We continue this till we get the desired degree of accuracy in the value of the root (upto a certain number of decimal points).
Fortran Program Example
convergence factor of 1 and is thus considered very reliable.| [Home] | [Features] | [TOC] | [Purchase] | [Sample Code] | [Web] | [Manuals] | [Errata] | [Links] |
| Last updated: 5/20/2003 |
Fortran Program For Bisection Method
which says that if a continuous function changes sign over an interval, there is at least one root of the function in that interval. Here is how to find a root using this method.- Assign end points for the 'root hunt'. Let's call them 'a' ad 'b'. The end points should be such that the value of the function, f at both points should be opposite in sign.i.e. f(a), f(b)<0. This is because we will search for a point within this limit that has zero value for the function or a point where the function crosses the x-axis of the Cartesian Plane. If the end points have the same sign, we can use the GO TO statement to read new values for a and b.
- We choose the mid-point of this interval. Now this mid-point, let's call it 'c', will have some value for the function, namely f(c). Evidently, f(c) will have a positive or negative sign unless it has the value zero in which case it is the root.
- If f(c) has a sign opposite to f(a) or f(b), we will continue searching the root between f(c) and that particular endpoint. Obviously, it cannot have a sign opposite to both as per our choice of a and b. Depending on which end has the opposite sign, either a will take the value of c or c will take the value of b.
- We continue this till we get the desired degree of accuracy in the value of the root (upto a certain number of decimal points).
Fortran Program Example
convergence factor of 1 and is thus considered very reliable.Fortran Program For Bisection Method Example
Now for the FORTRAN program,
!To find the root of a function using bisection method
program rootf
implicit none
real a,b,c,f,root
10 write (*,*) 'Give the range within which you wish to find a single root?'
read (*,*) a,b
write(*,*) 'The end points are'
write (*,*) 'a= ',a,'b= ',b
if (f(a)*f(b)>0) then !To make sure the end points have opposite signs
write (*,*) 'The function has same sign at both end points. Please, try again.'
go to 10
else
write (*,*) 'Finding roots in the range ',a,' to ',b
!To start computation
do
if (abs(f(a))<0.00001) then
root=a
exit
end if
if (abs(f(b))<0.00001) then
root=b
exit
end if
c=(a+b)/2.0 !To check the value of the function at the mid-point. This will anyway be checked again when the value of c is replaced the next time the loop runs
if (abs(f(c))<0.00001) then
root=c
exit
end if
if (f(a)*f(c)<0) then !To move end points closer to the root
b=c
else
a=c
end if
if (abs(b-a)<0.00001) then ! To exit the loop on getting the answer upto a certain number of decimal places
root=a
exit
end if
end do
end if
write (*,*) 'The root of x**2-x-5 in the range ',a,' to ',b,' is ',root !To display the result
end program rootf
!Subprogram to define the function, f
function f(x)
implicit none
real f,x
f=x**2-x-5 !You can change the function as per choice. Just make sure it is continuous
end function f
!To find the root of a function using bisection method
program rootf
implicit none
real a,b,c,f,root
10 write (*,*) 'Give the range within which you wish to find a single root?'
read (*,*) a,b
write(*,*) 'The end points are'
write (*,*) 'a= ',a,'b= ',b
if (f(a)*f(b)>0) then !To make sure the end points have opposite signs
write (*,*) 'The function has same sign at both end points. Please, try again.'
go to 10
else
write (*,*) 'Finding roots in the range ',a,' to ',b
!To start computation
do
if (abs(f(a))<0.00001) then
root=a
exit
end if
if (abs(f(b))<0.00001) then
root=b
exit
end if
c=(a+b)/2.0 !To check the value of the function at the mid-point. This will anyway be checked again when the value of c is replaced the next time the loop runs
if (abs(f(c))<0.00001) then
root=c
exit
end if
if (f(a)*f(c)<0) then !To move end points closer to the root
b=c
else
a=c
end if
if (abs(b-a)<0.00001) then ! To exit the loop on getting the answer upto a certain number of decimal places
root=a
exit
end if
end do
end if
write (*,*) 'The root of x**2-x-5 in the range ',a,' to ',b,' is ',root !To display the result
end program rootf
!Subprogram to define the function, f
function f(x)
implicit none
real f,x
f=x**2-x-5 !You can change the function as per choice. Just make sure it is continuous
end function f
Fortran Program For Bisection Method Overriding
Sample Output for the Bisection Method
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