Numerical method-Picards,Taylor and Curve Fitting.Keshav Sahu
Here i have given some topics which is related to numerical method and computing.I covered picards method, Taylors series method, Curve fitting of method of least square and fitting a non leaner curve.
Solve nonlinear equations using bracketing methods: Bisection and False Position
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Numerical method-Picards,Taylor and Curve Fitting.Keshav Sahu
Here i have given some topics which is related to numerical method and computing.I covered picards method, Taylors series method, Curve fitting of method of least square and fitting a non leaner curve.
Solve nonlinear equations using bracketing methods: Bisection and False Position
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
On the Numerical Solution of Differential EquationsKyle Poe
Report written to satisfy requirements of ENGR 219, Numerical Methods, as part of an independent study of the course. Topics range from multistep methods for ODE solution to finite element methods.
What is numerical differentiation?
What is finite difference?
How to apply that to boundary value problems?
#WikiCourses #Num001
https://wikicourses.wikispaces.com/Topic+Boundary+Value+Problems+-+Finite+Difference
Subject Title: Engineering Numerical Analysis
Subject Code: ID-302
Contents of this chapter:
Mathematical preliminaries,
Solution of equations in one variable,
Interpolation and polynomial Approximation,
Numerical differentiation and integration,
Initial value problems for ordinary differential equations,
Direct methods for solving linear systems,
Iterative techniques in Matrix algebra,
Solution of non-linear equations.
Approximation theory;
Eigen values and vector;
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMSroymeister007
This report provides a practical overview of numerical solutions to the heat equation using the finite difference method (FDM). The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation. Complete, working Matlab and FORTRAN codes for each program are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated. These sample calculations show that the schemes realize theoretical predictions of how their truncation errors depend on mesh spacing and time step. The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS). The codes also allow us to experiment with the stability limit of the FTCS scheme.
The finite volume method for diffusion problemsshivam choubey
Matlab code for diffusion problem.
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
Book by H. K. Versteeg and W. Malalasekera
(4.1 (page 119)
This project work is concerned with the study of Runge-Kutta method of higher order and to apply in solving initial and boundary value problems for ordinary as well as partial differential equations. The derivation of fourth order and sixth order Runge-Kutta method have been done firstly. After that, Fortran 90/95 code has been written for particular problems. Numerical results have been obtained for various problems. The main focus has been given on sixth order Runge-Kutta method. Exact and approximate results have been obtained and shown in tubular and graphical form
On the Numerical Solution of Differential EquationsKyle Poe
Report written to satisfy requirements of ENGR 219, Numerical Methods, as part of an independent study of the course. Topics range from multistep methods for ODE solution to finite element methods.
What is numerical differentiation?
What is finite difference?
How to apply that to boundary value problems?
#WikiCourses #Num001
https://wikicourses.wikispaces.com/Topic+Boundary+Value+Problems+-+Finite+Difference
Subject Title: Engineering Numerical Analysis
Subject Code: ID-302
Contents of this chapter:
Mathematical preliminaries,
Solution of equations in one variable,
Interpolation and polynomial Approximation,
Numerical differentiation and integration,
Initial value problems for ordinary differential equations,
Direct methods for solving linear systems,
Iterative techniques in Matrix algebra,
Solution of non-linear equations.
Approximation theory;
Eigen values and vector;
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMSroymeister007
This report provides a practical overview of numerical solutions to the heat equation using the finite difference method (FDM). The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation. Complete, working Matlab and FORTRAN codes for each program are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated. These sample calculations show that the schemes realize theoretical predictions of how their truncation errors depend on mesh spacing and time step. The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS). The codes also allow us to experiment with the stability limit of the FTCS scheme.
The finite volume method for diffusion problemsshivam choubey
Matlab code for diffusion problem.
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
Book by H. K. Versteeg and W. Malalasekera
(4.1 (page 119)
This project work is concerned with the study of Runge-Kutta method of higher order and to apply in solving initial and boundary value problems for ordinary as well as partial differential equations. The derivation of fourth order and sixth order Runge-Kutta method have been done firstly. After that, Fortran 90/95 code has been written for particular problems. Numerical results have been obtained for various problems. The main focus has been given on sixth order Runge-Kutta method. Exact and approximate results have been obtained and shown in tubular and graphical form
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
2. Methods of Analysis
• Classical or exact solution of GDE of motion
• Rayleigh's method
• Modified Rayleigh’s Method
• Rayleigh’s Ritz Method
• Approximate Method
– Finite difference method
– By lumping masses
– FEM
3. • The FDM is the approximate method for the
solution of vibration problem.
• The differential equation is the starting point
of the method.
• The continuum is divided in the form of mesh
& unknowns in the problem are taken at the
nodes.
• The derivatives of the equation are expressed
in the finite difference form.
• The differential equation, split in this discrete
form is applied at each node.
4. FINITE DIFFERENCE METHOD
• Let, variable ‘w’ is the function of x which is as
shown in the fig.
• The function is divided into equally spaced
interval of ‘h’.
• Station to the right are indicated as i+1,i+2 ….
and corresponding values of the function are
Wi+1, Wi+2 ….
• Station to the left are indicated as i-1,i-2 ….
and corresponding values of the function are
Wi-1, Wi-2 ….
5. • The first derivative is given by,
……. (1)
Above equation suggest that the slope of the curve between i+1 and
i-1 considered to be constant.
7. • Put equation (3) into equation (2)
we get,
…….. (4)
again diff. above equation 2 times w.r.t ‘x’
We get,
……. (5)
8. Free vibration of Beams
• The differential equation for the free vibration of
a beam is given by,
………(6)
• From equation (5) we get,
……(7)
Where m-mass per unit length
9. • For a uniform beam above equation becomes
……(8)
When it is expressed in finite difference form
…..(9)
Let,
λ =
we get,
10. • In order to study the free vibration of a beam, it is
divided into a number of segments.
• The finite difference equation is applied at each
node
• Boundary condition are then applied
• The resulting values are in the form of Eigen value
problem which on solution gives natural
frequencies and the mode shapes
11. Example
determine the fundamental frequency of the beam
of the given fig. by dividing it into four equal parts
and draw the first mode shape.
Solution:
The beam has to be divided into 4 equal parts and
the node numbers have been indicated in fig,
The deflection at nodes 1,2 and 3 are w1,w2,w3
resp.
Two ends are indicated as 0 and 4
The imaginary node beyond 0 has been shown as -1
and node beyond 4 shown as 5.
12. • The boundary condition at node 0 are,
W0 = 0 and = 0 …..(a)
Writing in the finite difference form,
w1 + w-1 = 0 ……(b)
13. • The boundary condition at node 4 are,
W4 = 0 and = 0 …..(c)
Writing above equation in finite difference form
W3=W5 …..(d)
Equation (b) & (d) relate the external nodes to internal
nodes.
Apply equation (7) to nodes 1,2 & 3 resp.
λ
14. Above equation is an Eigen value problem..
Solve the above determinant and find out the
lowest root is,
λ=0.72
Therefore
15. Assume w1=1 and substituting the value λ=0.72 in
the 2nd and 3rd eq. of (e)
5.26w2-4w3=4
-4w2+6.28w3=-1
On solving,
w2 =1.231
w3 =0.625
The first mode shape has been shown in fig,