Numerical integration Definition and 148 Threads

i want to find the minimum sum of this equation and find the t like using solver in Excel,but since the integration cannot be integrate directly,i didnt know how to use the numerical integration to apply for this problem. i want to find the value :let say when n=2, t_0=0 and t_n=1, so i need...

Hi, I've using numerical integration method (Simpson rule) to evaluate a definite integral in the interval [a,b]. I was wondering what is the ideal way to approximate the integral in the boundary [a,b) or (a,b] or (a,b) when for example, the function inside the integral does not exist at that...

hello, I have a problem with the use of quad function in Matlab for numerical integration. Let me try to explain on an example. When I want to find the integral of expression exp(-x^2/2) from 0 to infinity, where for the higher bound I use some very large number: Q =...

i am very new in matlab. and i need to calculate the arc lengh. My equation is arc length = integration of sqrt(d.*(k.^2-2).*sin(k.*t./2).^2 - d.*(k.^2-1).*sin(k.*t./2).^4 + 1); from 0 to 2.pi where, d=(0:.1:1) and k=(0:1:10) can anybody tell me whether it is possible to calculate this arc...

Hello I have a function which is very similar in shape to a Gaussian, except it is not a distribution and it is not analytic, so I can at best calculate a single point on the curve at a time. (In general it is a convolution of different distributions but this is not important). I need to find...

Hello--- I am reading a paper which describes a somewhat-unfamiliar mathematical procedure. The paper asks for a 2D spectrum U(t, \omega) of a signal s(t) which is calculated using the short-time Fourier transform (Gabor transform). This is reasonably straight-forward. However, the paper...

Hello-- I need to generate synthetic data to test an algorithm used to process data from an experiment. A synthetic wavelet is constructed using the following equations, but I am uncertain how to numerically evaluate the improper integral shown below. \[ u(t) = {\mathop{\rm...

Hi, I was wondering if anyone can point me to a general treatment of errors when doing numerical integration of measured variables? My problem is that I am integrating force with respect to displacement (of a piston) in an attempt to calculate work...and getting some impossible numbers...

Hi, I have an excel spreadsheet that calculates the pressure inside a piston chamber, that is a function of time. I want to calculate the distance the piston moves, this is my situation. P=F/A, therefore force on piston = PA F = M(piston).a so ma = PA, a = P(t)A/m its all numerical in...

Hi, Pretext: I have no formal background in MATLAB or maths in general, so apologies if any of the following doesn't make sense. I am also new to this forum, so apologies if this post is incorrect in any way. [n.b. I also posted this thread on mathhelpforum.com] Context: Ok, so I wanted to...

Homework Statement In brief, I am working on a stellar model. We started with these four equations: \delta q/\delta x = px^{2}/t \delta p /\delta x = -pq/tx^{2} \delta t /\deltax = -Cp^{1.75} / x^{2}t^{8325} \delta t /\delta x = -2q/5x^{2} In the model you switch to the 4th...

u := x (4 - y - x^2) v := y (-1 + x) (-2,0) du := (4 - y - 3 x^2) dx - x dy dv := y dx + (-1 + x) dy x := -2 + Cos[\[Theta]] y := 0 + Sin[\[Theta]] dx := -Sin[\[Theta]] dy := Cos[\[Theta]] Integrate[1/(2 \[Pi]) Expand[(u dv - v du)/(u^2 + v^2)], {\[Theta], 0, 2 \[Pi]}] If...

I've got a problem where I need to numerically integrate a multivariable function but I'm not sure how to do this. I'm more than familiar with how to numerically integrate a single variable function numerically but I have no clue how to do this for a multivariable function. For example let's say...

\int^{1}_{-1}f(x)dx = \sum^{n}_{j=-n}a_{j}f(x_{j}) Why does \sum_{j}a_{j} = 2 ? I know that the aj's are weights, and in the case of [-1,1], they are calculated using the roots of the Legendre polynomial, but I don't understand why they all add up to 2.

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

I want to integrate a function in 3D space, and then plot the integrated function, to compare with my analytical solution, I am using Fortran 90, I have no problem integrating, I am just not sure how I can plot the resulting function out. I am currently thinking about piecewise integration...

If I have a vector of data that is equally spaced in time. What is the best numerical method for integrating this data?

I have tried searching and have not come up with an answer to this question - but have come close in my own work (i think). Note: I want to solve this numerically, or by some formula. I am trying to solve this problem, save I have function f(x), the equation is not known. Its derivative...

What are some simple techniques to numerically integrate functions with poles?

Hi everyone, I am writing a simple code using Numerical Recipes (that bible of numerical method) to integrate using trapezoid rule the following integral int_pi/2_inf {sin(x)/x^2} dx I first make variable change y = 1/x to change limit of integration so that now the integral becomes...

We've covering numerical integration in one of my classes this semester, however I'm sort of at a loss as to how to deal with error in when using a taylor expansion for numerical integration, and also order of method (Big Oh?) and what exactly it means and was wondering if anyone could explain...

I'm doing some numerical integration using C++ with Visual Studio. Are there any free online libraries where I can find routines to help with this? If there are, what is recommended and would be compatible with VC++? I have looked at the GNU library, but from what I understand this only works on...

Hi everybody! I kindly request your help in optimizing the numerical integration of the following expression: \xi (r)=\frac{1}{2\pi ^2}\int_{-\infty}^{\infty}f(k)\cdot \sin(k\cdot r)\cdot dk f(k) vanishes outside the boundaries k=0 and k=2; I have got k and f(k) as float arrays, so we...

OK...this is a really trivial question, but I hope someone can help me here. I am working on building a segway-style robot that balances on two wheels, but I am having some difficulties integrating the data I receive from my gyro sensor. The sensor gives me the angular velocity, and I know...

Here is an integral (similar in form to the one) I want to evaluate: $$ \int_{r_1}^{r_2} R \left\{ \int_{x_1}^{x_2} Y(x,R)\, dx \right\}^2\,dR $$ This is my approach - please correct me because I don't think it's right: I treat R as a constant and evaluate the inner integral over some vector of...

Hi, I have a set of over 1000 field measurements as a function of Z. I want to multiply them by COS(Z) and integrate with respect to Z. I have tried using the quadl function but to no avail. Is what I want to do possible in Matlab (ie. is there a built in function for this) and if so...

Hello I have the following question in numerical integration in higher dimension. Any help/suggestion would be welcome. The integral is ( I am using maple notation ): int( int( int( int( int( int( f(x,y,z), z=-infinity..w), w=-infinity..infinity)...

Hello, I have a math problem that I think I've worked out properly, but I'm not entirely sure. The explanation is a bit lengthy, but I don't want to miss anything that might be pertinent. Essentially, I have a force equation F(t) that describes the acceleration of a body in two dimensions...

Hello. I've recently been using a few different numerical integration methods to solve a number of different problems, and as I looked into the integration algorithms, I realized that I don't understand them as well as I thought I did. I created a simple Excel workbook that calculates the...

The trapezoidal rule for numerical integration is based on the idea that when we partition our larger interval into subintervals, we can approximate the area over each subinterval by calculating the area of the trapezoid formed by connecting the value of the function at the left and right...

There isn't an applied mathematics thread so i'll post this here. I'm an undergraduate and I have a presentation for my numerical methods/matlab class . I'm looking for examples of 1)Integrals which are easier/faster to integrate numerically than do evaluate using their antiderivatives...

Hi. Can anyone tell me where to find information on how to evalutate a principal value integral numerically? When I say principal value, I mean an integral where a certain point is excluded from the domain of integration. In my case, the integrand is singular in this point.

Given any distribution of mass, the gravity at any point outside it can be calculated by dividing the mass into infinitesimal masses, and adding up the gravity due to each. Doing that, I faced a problem on the surface of an object: no matter how small you make the integration step, near the...

there are 5 examples as follows: %%% example01 %%%% z=linspace(-0.1,0.1); a=0.1; kesi=(z+sqrt(z.^2-a^2))./a; for j=1:length(z) f=@(b) log(1-((b+sqrt(b.^2-a^2))./a)./kesi(j)); I(j)=quadl(f,-0.1+eps,0.1+eps,1e-8); end %%% example02 %%%% z=linspace(-0.1,0.1); a=0.1...

Does the Simpson's rule of numerical integration (\frac{1}{3}h\left( {f_0 + 4f_1 + f_2 } \right)) give exact values for all polynomials to a third degree i.e., linear functions, quadratic functions, and cubic functions? Is there a better method for numerical integration approximation? One...

Homework Statement Given the system x'(t)=-ax(t)+ky(t)+g y'(t)=lx(t)-by(t)+h If g=h=0, a) Find the equilibrium b) Show that if ab-lk does not equal 0, the steady state found in (a) is the only solution c) choose a,b,l,k such that ab-lk > 0. Find numerically the solution of the system...

I figured it out. Thanks!

we've a basic numerical integration assignment, using simpsons/trapezium rule to calculate some non analytical function. Logic suggests that you use as many "strips" as possible (ie. as small a value of dx as possible) to estimate the value of the integral, however I've seen some graph some...

How can I speed up some calculations in maple? I have a function f(A)=A*I_0(A)/I_1(A)-c0*log(A/I_1(0))-1 I_0(A)=NInt(exp(A*c1*cos(x)*cos(y)*cos(z)), 0..2*Pi) I_1(A)=NInt(cos(x)*cos(y)*cos(z)*exp(A*c1*cos(x)*cos(y)*cos(z)), 0..2*Pi) c0 and c1 are known constants. I need to solve the...

using composite trapezoidal rule with n=4 how can i get a bound for the error of I=integration tan(x) from x=0 to x=pi/2 i know that the term of error in comp trapezoidal rule is (b-a)/12 h^2 f''(eita) i got the second derevative of tanx to be 2sec^2 x tanx then i don't know with what value...

Are there many interesting computational physics problems out there? Are there any comet trajectories that will deviate from a standard ellipse? For some reason plotting the path of a baseball just doesn't spark my interest.

Hi all, I am having trouble numerically integrating a function using Maple 10. Here is a bit of background on the problem: This problem is asking for two plots, one of the velocity of a sounding rocket with respect to time, and the other being the height of the sounding rocket with...

Im supposed to solve integral 10 to +infinity ((sin(1/x)/(1+x^3))dx with error precision of e=0.5*10^-4. Can someone please give me detailed explenation of solving this. (Supposedly by Simpson but i get lost in the way. P.S. sorry for bad spelling and lack of proper formula notions.

Im supposed to solve integral 10 to +infinity ((sin(1/x)/(1+x^3))dx with error precision of e=0.5*10^-4. Can someone please give me detailed explenation of solving this. (Supposedly by Simpson but i get lost in the way. P.S. sorry for bad spelling and lack of proper formula notions.

Hello there, I've not been here in a while, but I'm stuck doing this integration and wondered if some of you kind people would help :smile: \int_0^\infty \frac{1} {(1+x)\sqrt{x}} dx (appologies for the lack of spacing in there...) anyways, I know that when x tends to infinity, the...

I am performing the numerical integration of finding the area of 1/x dx from 0 to 2... using Simpson's rule of n = 6. What will I do in this problem like this since 0 to be evaluated in the f(x) = 1/x is undefined?

Does anyone have a program for numerical integration in fortran??

In fact for multiple integrals ..i know that montecarlo methods are used..but can these be generalized to get a infinite dimension integrals.. (integration over R**n where n tends to infinity)..can be they generalized to fractional dimensional integration?..(integraton on R**d with d not an integer)