Ganitagya Gyanam

Predictor-Corrector Method is one of the important method as it predicts the values and then corrects itself.  This method is different from the Runge-Kutta method as the Runge-Kutta method needs only the information of only the previous one value. Second, the Predictor-Corrector method requires less computation at each step than the Runge-Kutta method . In this article, we will discuss two methods. One is Milne's method and the other is the Adams-Bashforth method. We discussed a few solved examples of both the methods and in the end we provide a few unsolved questions for practice. Conclusion: So, we have discussed here the Predictor-Corrector methods, that is, Milne's method and Adams-Bashforth formula and discussed a few numerical based on these methods. Try to solve these numerical to understand the procedure of the Predictor-Corrector method.

Runge-Kutta Method:  The objective of the Runge-Kutta method is that it is used to solve the ordinary differential equation . Small the size of h we get a more accurate solution of the ordinary differential equation. In this article, we have discussed the Runge-Kutta method that is First-order Runge-Kutta method Second-order Runge-Kutta method Third-order Runge-Kutta method Fourth-order Runge-Kutta method Lastly, we have discussed a few examples depending on the Runge-Kutta method also provides a few examples for practice. Thus, we can conclude that the most commonly used method for solving the first-order initial value problems is the classical Runge-Kutta method of fourth-order because using two slopes in the method, we can obtain methods of second order, which are called as the second-order Runge-Kutta methods. The method has one arbitrary parameter, whose value is suitably chosen.  The methods using four evaluations of slopes have two arbit...

Numerical Solution of ODE Using Taylor and Euler method: First of all we discussed the ordinary differential equation and then we discuss the methods for solving the ordinary differential equation of first order. In this post, we discuss the following concepts. Ordinary differential equations Numerical methods of solution of ordinary differential equations Taylor Series method Euler Method Modified Euler Method Lastly, we have discussed a few questions depending on these methods. Also, we have given a few questions for practice.

Iterative methods for polynomial equations have been discussed in this article. In which we have discussed the following methods: 1. Birge-Vieta Method: 2. Graeffe's Root Squaring Method: 3. Laguerre Method 4. Bairstow Method After the discussion of these methods, we provided the numerical based on these methods . So that you will be able to understand the concept of the methods.