2015年8月25日 · $\begingroup$ What I don't see in any of the answers: while for ODE the initial value problem and some boundary value problems have unique solutions (up to some constants at least), for PDE, even linear ones, there can be infinitely many completely different solutions, for example time dependent Schrodinger equation for some potentials admits a lot of mathematically valid, but unphysical ...

2018年10月9日 · So the temperature of the bar satisfies a PDE - the heat equation. As time goes by, the temperature of the bar approaches an equilibrium state where its temperature does not depend on time, but only on the distance along the bar. The equilibrium temperature (as a function of distance only) can be found by solving an ODE.

2004年7月8日 · I've heard Maple is better for various tasks, such as symbolic manipulation, ODE, and PDE solving. However, I've also heard that Mathematica is superior in the field of symbolic integration. I've only used Mathematica (versions 4 and 5), and I'm rather curious about Maple (since I will be using it this upcoming year).

2013年11月9日 · The ODE looks like a proper math course. The PDE looks like a fairly gentle tour around a few standard equations and numerical methods (but not necessarily methods that anybody actually uses in the 21st century!) I would say the ODE course is harder and you would learn more, and what you will learn applies to PDEs as well as ODEs.

2013年7月18日 · Here is the description for the actual ODE (which is higher than differential equation and pde. Math 430 Ordinary Differential Equations I: Picard existence theorem, linear equations and linear systems, Sturm separation theorems, boundary value problems, phase plane analysis, stability theory, limit cycles, and periodic solutions.

2008年12月7日 · A Spectral Theorem to Convert PDE into ODE. May 30, 2018; Replies 2 Views 2K.

2016年6月8日 · If you use the straightforward finite differencing for a PDE, you usually encounter numerically unstable behavior, which means that the numerical errors in your solution grow exponentially as a function of the time variable t. That is why there are Crank-Nicolson schemes and semi-implicit schemes for solution of PDE:s.

$\begingroup$ If the ODE has the unknown function and/or its derivative(s) as an argument of a trigonometric, hyperbolic trigonometric, exponential, logarithmic, and/or n-th root function, the ODE is non-linear. If the ODE has a product of the unknown function times any of its derivatives, the ODE is non-linear.

2006年2月14日 · What is so special in a partial differential equation that it requires so many methods as follows. What is the difficulty that makes the ode and pde different in their solution 1)fem 2)bem 3)fdm 4)fvm

2013年2月12日 · ODE=Ordinary Differential Equations ( ;O I hope this is right, I took a course on... Insights Blog -- Browse All Articles -- Physics Articles Physics Tutorials Physics Guides Physics FAQ Math Articles Math Tutorials Math Guides Math FAQ Education Articles Education Guides Bio/Chem Articles Technology Guides Computer Science Tutorials