Numerical Methods for Science and Engineering.

1962 ◽  
Vol 16 (77) ◽  
pp. 114
Author(s):  
D. M. Y. ◽  
Ralph G. Stanton
Keyword(s):  
Numerical Methods ◽  
Science And Engineering

Numerical Methods for Science and Engineering (R. G. Stanton)

SIAM Review ◽  
1961 ◽  
Vol 3 (4) ◽  
pp. 342-342
Author(s):  
Preston C. Hammer
Keyword(s):  
Numerical Methods ◽  
Science And Engineering

scholarly journals Numerical Modelling on the Influence of Source in the Heat Transformation: An Application in the Metal Heating for Blacksmithing

2021 ◽  
Vol 7 (2) ◽  
pp. 97-101
Author(s):  
H. P. Kandel ◽  
J. Kafle ◽  
L. P. Bagale
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Numerical Technique ◽  
Heat Equations ◽  
Science And Engineering ◽  
Physical Problems ◽  
Different Temperatures ◽  
The One ◽  
Heat Transformation

Many physical problems, such as heat transfer and wave transfer, are modeled in the real world using partial differential equations (PDEs). When the domain of such modeled problems is irregular in shape, computing analytic solution becomes difficult, if not impossible. In such a case, numerical methods can be used to compute the solution of such PDEs. The Finite difference method (FDM) is one of the numerical methods used to compute the solutions of PDEs by discretizing the domain into a finite number of regions. We used FDMs to compute the numerical solutions of the one dimensional heat equation with different position initial conditions and multiple initial conditions. Blacksmiths fashioned different metals into the desired shape by heating the objects with different temperatures and at different position. The numerical technique applied here can be used to solve heat equations observed in the field of science and engineering.

MATLAB® Functions for Numerical Analysis and Their Applications in M&T

2021 ◽  
pp. 141-165
Keyword(s):  
Numerical Analysis ◽  
Friction Coefficient ◽  
Numerical Methods ◽  
Nonlinear Equations ◽  
Science And Engineering ◽  
Pressure Angle ◽  
Angle Function

The chapter presents the MATLAB® commands that realize numerical methods for solving problems arising in science and engineering in general and in the field of mechanics and tribology (M&T) in particular. The most commonly used commands along with some information on numerical methods are explained. The topics of the chapter include interpolation and extrapolation, solving nonlinear equations with one or more unknowns, finding minimum and maximum, integration, and differentiation. All described actions are explained by examples from the field of M&T. At the end of the chapter, applications are presented; they illustrate how to interpolate the friction coefficient data, calculate elongation of a scale with two springs, determine the maxima and minima of the pressure-angle function, and solve some other M&T problems.

scholarly journals Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Uğur Kadak ◽  
Muharrem Özlük
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Generating Functions ◽  
Kutta Method ◽  
Science And Engineering ◽  
Runge Kutta Method ◽  
Wide Range ◽  
Runge Kutta

Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions.

Numerical solution of Burgers’ equation using Biorthogonal wavelet-based full approximation scheme

2019 ◽  
Vol 08 (01) ◽  
pp. 1850030 ◽  
Author(s):  
S. C. Shiralashetti ◽  
L. M. Angadi ◽  
A. B. Deshi
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Test Problem ◽  
Approximation Scheme ◽  
Burgers Equation ◽  
Wavelet Filter ◽  
Biorthogonal Wavelet ◽  
Science And Engineering ◽  
Cpu Time

Recently, wavelet-based numerical methods have been newly developed in the areas of science and engineering. In this paper, we proposed a full-approximation scheme for the numerical solution of Burgers’ equation using biorthogonal wavelet filter coefficients as prolongation and restriction operators. The presented scheme gives higher accuracy in terms of higher convergence in less CPU time, which has been illustrated through the test problem.

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