ODE Boundary Value Problems and Finite Differences
Steady State Heat and Diffusion:
If we regard as the movement of heat in a long thin object (like a metal bar) it is known that the temperature u(x, t) at a location x and time t convince the partial differential equation:
ut− uxx = g(x, t),
Where g(x, t) is the consequence of any external heat source. The similar equation as well describes the diffusion of a chemical in a one-dimensional environment. For illustration the environment might be a canal and then g(x, t) would stand for how a chemical is introduced.
Sometimes we are interested merely in the steady state of the system, supposing g(x, t) = g(x) and u(x, t) = u(x). In this case:
uxx= −g(x).
This is a linear second-order ordinary differential equation that we could discover its solution exactly if g(x) isn’t too complicated. If the environment or else object we consider has length L then typically one would have conditions on each end of the object such as u(0) = 0, u(L) = 0. Therefore instead of an initial value problem we have a boundary value problem or BVP.
Beam With Tension:
Consider a simply supported beam with modulus of elasticity E moment af inertia I, a uniform load w and end tension T. If y(x) denotes the deflection at every point x in the beam then y(x) satisfies the differential equation:
With boundary conditions y(0) = y(L) = 0. This equation is nonlinear as well as there is no hope to solve it exactly. If the deflection is little then (y′)2 is negligible compared to 1 and the equation approximately simplifies to:
This is a linear equation as well as we can find the exact solution. We can rewrite the equation as:
y′′ − αy = βx(L − x),
A merely supported beam with a uniform load w and end tension T
Where
α =T/EI and β =w/2EI
and then the precise solution is:
Latest technology based Matlab Programming Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Matlab Programming help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Matlab Programming, project ideas and tutorials. We provide email based Matlab Programming help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Matlab Programming. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Matlab Programming Homework help and assignment help services. They use their experience, as they have solved thousands of the Matlab Programming assignments, which may help you to solve your complex issues of Matlab Programming. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
Principles of independent assortment tutorial all along with the key concepts of Mendel's Second Law of Inheritance, Genotypes and Mendel's first law
www.tutorsglobe.com offers Functional Programming Languages homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
General Characteristics of Microorganisms tutorial all along with the key concepts of functions of Microorganisms, Bacteria, Fungi, Viruses, Algae and Protozoa
tutorsglobe.com the uncertainty principle assignment help-homework help by online atomic structure tutors
Directors’ share option schemes have been a popular method of rewarding the directors of large listed companies and several arguments have been put forward to support their use.
www.tutorsglobe.com offers water solubility homework help, water solubility assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
heat change tutorial all along with the key concepts of heat change under constant volume, enthalpy and enthalpy changes, relation between cp and cv of an ideal gas
tutorsglobe.com properties of fluorine assignment help-homework help by online halogen family tutors
kinetics and equilibrium tutorial all along with the key concepts of factors influencing reaction rate, experimental methods, kinetics and the equilibrium constant and free energy
tutorsglobe.com different biological databases assignment help-homework help by online biological database tutors
www.tutorsglobe.com offers atomic structure homework help, atomic structure assignment help, online tutoring assistance, physical chemistry solutions by online qualified tutor's help.
We offer top-class Linear regression and Correlation Assignment Help from subject matter experts at viable prices to score A++ with quality solutions.
www.tutorsglobe.com offers distribution of factory overheads homework help, assignment help, case study, writing homework help, online tutoring assistance by accounting tutors.
tutorsglobe.com proteins assignment help-homework help by online cell membrane tutors
the working of fan is which they do not in fact decrease the temperature of the room but because of the circulation and wind motion they result in surface cooling and provide a breezy feeling.
1930892
Questions Asked
3689
Tutors
1459742
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!