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Match the following items

(i) Newton-Raphson | (a) Integration |

(ii) Runge-Kutta | (b) Root finding |

(iii) Gauss-Seidel | (c) Ordinary Differential Equations |

(iv) Simpson's Rule | (d) Solution of Systems of Linear Equations |

+1 vote

i-b,ii-c,iii-d,iv-a

==> Newton-Raphson method. it is a iterative process follows a set guideline to approximate one root, considering the function, its derivative, and an initial x-value.

The Newton-Raphson method uses an iterative process to approach one root of a function.The specific root that the process locates depends on the initial, arbitrarily chosen x-value.

https://www.shodor.org/UNChem/math/newton/

and one good example is https://gateoverflow.in/2627/gate1995-2-15

==>Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods

==>Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.

https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method

==>Simpson's rule is a Newton-cotes formula for approximating the integral of a function using quadratic polynomialhttp://mathworld.wolfram.com/SimpsonsRule.html

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