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● Bisection method: This method is important as it is the root finding method and it bisects the given interval in the repeated manner by selecting the sub-interval. This is known as the interval halving method or the binary search method.
● Newton’s method: The Newton’s method or the Newton Raphson method is used for the better approximation. It is used as the example of the root finding algorithm.
● Numerical Linear Algebra: This part is related to find out the algorithms to perform the computational methods including the matrix operation. It is the basic part in different disciplines like computational science, telecommunications etc.
● Iterative methods: This mathematical procedure is used to generate the approximate solutions for different problems.
● Computing roots of Polynomials: This process is used to find out the roots of the continuous functions. Basically, the roots can’t be computed properly and it is not possible to express it in the closed form.
● Approximation theory: Approximation theory is concerned with the approximation of the complex function into the simpler function. It also characterizes the errors also.
● R-K method: In numerical computation, the R-K method includes the Euler method by employing the temporal discretization for the solutions of the ODE.
● Trapezoidal method: This rule is used to find out the approximation of the definite integral. It works by having the approximation of the area under the graph. This graph is drawn from the function and this function is defined as the trapezoid.
● Computational fluid dynamics: the computational fluid dynamics is the applied tool in order to generate the solutions for the flow of the fluid without the interaction. In this analysis, the physical properties of the fluid flow are examined. These properties are important as they help to generate the solution of the physical phenomenon which is associated with the system, should be considered simultaneously.
● High order differential equations: The higher order differential equations are also the part of the numerical analysis system. These kinds of the differential equations can be solved by different numerical methods and the procedures.
● Approximating the Eigen-values: In the numerical analysis, the Eigenvector and the Eigen-values are the most important.
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Numerical methods and the numerical analysis algorithm is the major field in the mathematics. It is basically the study of the algorithm and it uses different kinds of numerical calculations to have the solution of the issues which are interrelated to the arithmetical analysis. The algorithms of the interpolation are attached to these kinds of the analysis which are used for the solution of the differential equations.
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This subject is useful in every field of the academic career including the engineering and the science. It is useful in order to evaluate the motions of the heavenly figures. It is used to calculate the problems of the linear algebra. This is also used in the field of biology. In order to solve the higher order differential equations, the interpolation algorithms are used. We solve the problems by using different numerical analysis methods.
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● The series expansion
● IVT (Initial Value Theorem)
● Boundary value problem
● Spectral methods solving
● Secant method
● Numerical integration
● Gaussian quadrature
● Richards’s methods
● Iterative method
● Cauchy problems
● Conjugate gradient method
● Absolute stability
● Truncation error
● Partial differential equation
● Newton method
● Applied mathematics
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