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Replies to This Discussion

Please Discuss here about this GDB.Thanks

Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

start discussion plz....

Dear Students Don’t wait for solution post your problems here and discuss ... after discussion a perfect solution will come in a result. So, Start it now, replies here give your comments according to your knowledge and understandings....

kia jo book me 2,3 method diay huay hn whe use krnay hn ?is k ilawa kr lain t frq to nhi parta?.......book me simpson 3/8 kch better lgta hai

yes i agree with you

i think Newton-Cotes Integration methods (Trapezoidal rule) and its improved method Romberg's Integration is best in this case

Idea solution 

inear multistep method:

Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution. Single-step methods (such as Euler's method) refer to only one previous point and its derivative to determine the current value. Methods such as Runge-Kutta take some intermediate steps (for example, a half-step) to obtain a higher order method, but then discard all previous information before taking a second step. Multistep methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Consequently, multistep methods refer to several previous points and derivative values. In the case of linear multistep methods, a linear combination of the previous points and derivative values is used.

 fivestar1122 simpson 3/8 rule me error k chances less hotay hn than Trapezoidal rule...

Numerical integration aims at approximating definite integrals using numerical techniques. There are many situations where numerical integration is needed. For example, several well defined functions do not have an anti-derivative, i.e. their anti-derivative cannot be expressed in terms of primitive function. A popular example is the function e��x2 whose anti-derivative does not exist. This function arises in a variety of applications such as those related to probability and statistics analyses. Furthermore, many applications in science and engineering are represented by integral differential equations that require a special treatment for the integral terms (e.g. expansion, liberalization, closure …).
Therefore, numerical integration does not only provide a means for evaluating integrals numerically, but also grants us the ability to approximate special functions that are defined in terms of integrals. Without loss of generality, there are two classes of problems where numerical integration is needed. In the first class, one wishes to evaluate the integral of a well defined function. In this case, the integrand can be evaluated a various points because and numerical integration techniques help define the optimum number of these points as well as their locations. The second class of problems for applying numerical integration is found in differential equations the most common of which are those that express conservation principles. For example, the population balance equation, a well known partial

done ....

kia is gdb wale question ko solve b krna he ya just ye batna he k konsa method best he ???????

just describe method yehi solution hu gha

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