What's the difference between an initial value problem and a boundary value problem? Ask Question. Asked 8 years, 6 months ago. Active 1 year, 1 month ago. Viewed 35k times. I solve both problems the same way. I don't really understand the theory, I guess. Gladstone Asder Gladstone Asder 1, 4 4 gold badges 15 15 silver badges 23 23 bronze badges. Add a comment. Active Oldest Votes. Scientifica 8, 4 4 gold badges 18 18 silver badges 41 41 bronze badges.
Muhammad Tariq Muhammad Tariq 61 1 1 silver badge 1 1 bronze badge. Mohammad shehryar Mohammad shehryar What's the point of providing an answer to a question posted years ago and which has an accepted answer? Zainab ameer ali Zainab ameer ali 1. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. The intent of this section is to give a brief and we mean very brief look at the idea of boundary value problems and to give enough information to allow us to do some basic partial differential equations in the next chapter.
Now, with that out of the way, the first thing that we need to do is to define just what we mean by a boundary value problem BVP for short. With initial value problems we had a differential equation and we specified the value of the solution and an appropriate number of derivatives at the same point collectively called initial conditions.
For instance, for a second order differential equation the initial conditions are,. For second order differential equations, which will be looking at pretty much exclusively here, any of the following can, and will, be used for boundary conditions.
We will also be restricting ourselves down to linear differential equations. We will, on occasion, look at some different boundary conditions but the differential equation will always be on that can be written in this form. None of that will change. The changes and perhaps the problems arise when we move from initial conditions to boundary conditions. One of the first changes is a definition that we saw all the time in the earlier chapters. If any of these are not zero we will call the BVP nonhomogeneous.
It is important to now remember that when we say homogeneous or nonhomogeneous we are saying something not only about the differential equation itself but also about the boundary conditions as well. When solving linear initial value problems a unique solution will be guaranteed under very mild conditions.
In that section we saw that all we needed to guarantee a unique solution was some basic continuity conditions. With boundary value problems we will often have no solution or infinitely many solutions even for very nice differential equations that would yield a unique solution if we had initial conditions instead of boundary conditions. In fact, a large part of the solution process there will be in dealing with the solution to the BVP.
Or maybe they will represent the location of ends of a vibrating string. So, the boundary conditions there will really be conditions on the boundary of some process. We know how to solve the differential equation and we know how to find the constants by applying the conditions. Notify me of new comments via email. Notify me of new posts via email.
Create a free website or blog at WordPress. Falling for Alien ». This is what they say… i just copy-pasted it tehehe dextercioby said: It all depends on what the variables of the unknown function in the PDE are. Share this: Twitter Facebook. Like this: Like Loading Leave a Reply Cancel reply Enter your comment here Fill in your details below or click an icon to log in:.
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