What is Initial conditions: Definition and 133 Discussions

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). For a system of order k (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension n (that is, with n different evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace the system's variables forward through time.
In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time. In continuous time, the problem of finding a closed form solution for the state variables as a function of time and of the initial conditions is called the initial value problem. A corresponding problem exists for discrete time situations. While a closed form solution is not always possible to obtain, future values of a discrete time system can be found by iterating forward one time period per iteration, though rounding error may make this impractical over long horizons.

View More On Wikipedia.org
Recent contents Top users
  1. D

    Integrating factor problems (differential equation with initial conditions)

    Homework Statement Find general solution of equation (t^3)y' + (4t^2)y = e^-t with initial conditions: y(-1) = 0 and t<0 book answer gives y = -(1+t)(e^-t)/t^4 t not = 0 Homework Equations The Attempt at a Solution (t^3)y' + (4t^2)y = e^-t get integrating...
  2. D

    Solve Diff. Eq. w/ Initial Conditions: y' + 2y = te^-2t | Homework Help

    Homework Statement Solve the differential equation: y' + 2y = te^-2t with initial conditions y(1) = 0? Please show me what I am doing wrong... (or right).. also please don't show me shortcut i need to know where I am going wrong thanks. Homework Equations The Attempt at a...
  3. R

    Solving the Heat Equation for Initial Conditions

    Problem: u (sub t) = (1/2)u (sub xx) find the solution u(x,t) of the heat equation for the following initial conditions: u(x,0) = x u(x,0) = x^2 u(x,0) = sinx u(x,0) = 0 for x < 0 and 1 for x>=0 i'm really flying blind here. I've taken differential equations years ago but nothing...
  4. B

    Solving PDE with Initial Conditions for ϕ(x,t)

    Hi, I have a problem that I am working through, and I am at a point where I'm not sure what to do. I am solving a PDE using the method of characteristics. This has given me the solution ϕ(x,t)=F(x+(3ϕ^2-1)t) "for any function " F I have the initial conditions...
  5. J

    Engineering Initial Conditions of Circuit with SC & OC: Confused?

    This is the circuit at t(0-); Initial conditions need to be determined: Capacitor is replaced by an open circuit and inductor is replaced with a short circuit: These are the initial conditions I get: I through inductor (0-) = 3 A V across capacitor ( 0-) = 0 ( in parallel w/ SC)...
  6. apeiron

    Vagueness as a model of initial conditions

    This thread will attempt to bring together "vagueness" based approaches to going beyond the standard model. Vagueness gives a different way to model the Universe's initial conditions. (And also quantum indeterminacy, the two being not un-related). Vagueness in logic means indistinct...
  7. M

    Find r(t): Given Initial Conditions

    Homework Statement Given \vec{}r"(t)= 6i-4cos (2t)j+ 9e3tk, r'\vec{} (0)= 4i +3k and r\vec{}(0)=j+k, find r\vec{}(t). Homework Equations The Attempt at a Solution I will appreciate any ideas how to start this problem. Thank you.
  8. W

    Progressive wave with initial conditions f(x,0)=0, f'(x,0)=g(x)

    Consider a long straight string that is given an initial impulse. The transverse displacement of the string y(x,t) satisfies the initial condition: y(x,0) = 0 and y'(x,0) = G(x) Show that the solution to the wave eq'n satisfying the intitial condition is y(x,t) = 1/2v[H(x+vt)-H(x-vt)]...
  9. S

    Solving ODE: y = $\sqrt {x\ln (x)}$ w/ Initial Conditions

    Homework Statement given this ODE with initial conditions y(1)=0 \[ (x + y^2 )dx - 2xydy = 0 \] Homework Equations solving this ODE gives us \[y = \sqrt {x\ln (x)} \] as we can see this equation is true only for x>=1 in order to use the theorem on existence and uniqueness we isulate...
  10. T

    MATLAB Setting Initial Conditions for ode45() with f(1.5) Known

    Hey guys, I was just wondering if anyone knows how to set the initial conditions for ode45() if you know f(1.5) but NOT f(0) Currently I have >> ode45(f, [0 1 1.8 2.1], [1.5 .5]) But this creates the following error: ? Error using ==> funfun/private/odearguments @(T,Y)...
  11. A

    LC Circuit: Initial Conditions and Switch

    Hello guys. I have a simple question regarding an LC circuit. Imagine a voltage source V_0, a capacitor C and an inductor L, all hooked up in series. I know that the equation governing the behvior of the system is V_0=\frac{1}{C}q(t)+L\ddot{q}(t), and hence q(t)=A\cos \omega t +...
  12. quasar987

    Solving the PDE u_(xy) = ku with some initial conditions

    Homework Statement Does anyone know how to solve this PDE for u:R-->R and some initial conditions? u_{xy}=ku where k is a positive constant. Or this one, also for u:R-->R and some initial conditions: u_{tt}=u_{xx}-Ku where K is a positive constant.The Attempt at a Solution I can solve the...
  13. S

    Wave equation PDE, can't match initial conditions

    First post, hooray! Undergrad nuke engineer here, trying to figure out a really annoying PDE. My notation for U_xx = 2nd partial of U with respect to x, U_tt = 2nd partial of U with respect to t, etc. Homework Statement I'm working a nonhomogenous PDE with homogeneous initial and boundary...
  14. Y

    Boundary conditons and initial conditions of a vibrating rod

    Finding the vibrational motion of a rod. A uniform rod of length l is compressed from both ends so that its new length becomes l(1-2 \epsilon). The compression force is then removed and the rod is left to vibrate freely. Find the subsequent vibrational motion of the rod. What are the...
  15. P

    Using JPL Horizons to Obtain Inertial Positions and Velocities: A Tutorial

    Hi guys, help me. I have a code for integrate the equations of motion of three bodies in a inertial frame, and in cartesian coordinates (x, y, z, vxi, vyi, vzi), i=1,2,3. The question is, how can i use the data of JPL Horizons to obtain positions and velocities in a inertial frame?
  16. O

    Analyzing Motion of Mechanical System with Initial Conditions

    Determine the motion of this mechanical system- *Pic attached* satisfying the initial conditions :- y1(0) = 1 y2(0) = 2 y1'(0) = -2*sqrt(6) y2'(0) = sqrt(6) I need to find equations for y1(t) and y2(t). Please help :D PS ideal springs, point masses cannot collide, y1 and y2 are...
  17. K

    Find the particalur equation for the given initial conditions

    Find the particleur equation for the given initial conditions:- 1/2y'' + y' + 13y = 0 ; y(0) = 5, y'(0) = 0 The only method I know how to solve these doesn't seem to work. Any help is much appreciated.
  18. P

    Do Initial Conditions for PDEs Need to Satisfy Governing Equations?

    I would really like to know whether initial conditions given to a time evolution PDE has to satisfy the governing equations. For example, if I have to solve numerically an incompressible flow equation do I need to give initial solution for the velocity field which is divergence free so as to...
  19. H

    Solving Recurrence Relation w/ Initial Conditions for n-digit Sequences

    hello any one can help me with this question thanx (a) Find a recurrence relation for the number of n-digit sequences over the alphabet {0, 1, 2, 3, 4} with at least one 1 and the first 1 occurring before the first 0 (possibly no 0’s). (b) What are the initial conditions? (c)...
  20. H

    Initial conditions of our universe

    What were they dependent on?
  21. P

    Continuous String; Initial Conditions; Normal Modes

    Homework Statement Discuss the motion of a continuous string when the initial conditions are q'(x,0) = 0 and q(x,0) = Asin(3πx/L). Resolve the solution into normal modes. Show that if the string is driven at an arbitrary point, none of the normal modes with nodes at the driving point will be...
  22. H

    Initial conditions for stability

    The general solution fo the following equations: x'=2x-3y y'=x-2y Is, x=4C1e^2t, y=C1e^2t-3C2e^-2t They ask for me to list a set of initial conditions (xo, yo) for which the solution is stable, i.e, (x, y)-->(0,0) for large t. I don't understand this part of the problem.
  23. P

    Exploring Position Derivatives of Wave Function Initial Conditions

    When doing the initial conditions of the velocity of the wave function, why do they have a position (x) derivative (i.e. cF'(x)-cG'(x)=h(x)). It appears in here. http://en.wikipedia.org/wiki/D%27Alembert%27s_formula How someone explain how the c came about and why position derivatives are...
  24. L

    Exploring Initial Conditions for ODE Solution

    Hi, World! Nice place here! My first post in this forum. :smile: I've got a short question for a start. If we wish to evaluate the constants for the general solution x(t)=C_1e^{-{\lambda_1}t}+C_2e^{-{\lambda_2}t} of this ODE: \ddot{x}+2{\gamma}\dot{x}+{{{\omega}_0}^2}x=0 we can choose the...
  25. B

    Sensitive dependence on initial conditions

    Hi. I'm starting a project on chaos very soon and I was just wondering... One of the distinguishing features of a "chaotic system" is the sensitive dependence on initial conditions. It is stated that if we knew the initial conditions with infinite precision we would also be able to...
  26. J

    Solving a Quadratic Equation with Initial Conditions

    Ok, the question I have is attached. What I have done is found the general solution: (Question was seperable, so it was easy) y = x^2 - 2x + c But I don't kwow what/how to do is finding the initial conditions where there are: (a) No solutions (b) more than one solution (c) precisely...
  27. Pengwuino

    Finding the Solution to a Differential Equation with Initial Conditions

    Ok I have a problem here. I have gotten to the unfortunate point where I feel like I'm nearly done, Mathematica has given me a solution that is correct… but of course, I can't figure out how I was suppose to get from point A to B. I currently have: 2x - 6y\sqrt {x^2 + 1} \frac{{dy}}{{dx}} =...
  28. M

    Proving the superposition of initial conditions gives superposition of motion

    I have a problem that says to prove the superposition of initial conditions gives superposition of corresponding motion for two coupled oscillators. My question is: What do they mean by coupled oscillators? Do they mean coupled pendulums? Double LC circuits? If it's coupled pendulums are...
  29. S

    Sensitive Dependence on Initial Conditions

    This new paper in Nature Genetics: http://www.nature.com/ng/journal/v37/n8/abs/ng1608.html suggests that considerable variance in lifetimes of C. Elegans with controled, identical genomes, is caused by an essentially random variable; the first encounter with a certain chemical in its...
  30. C

    Initial Conditions of an Undamped Forced Harmonic Oscillator

    The equation of motion of an undamped harmonic oscillator with driving force F=F_ocos(\omega*t) is x(t) = Acos(\omega_0*t) + Bsin(\omega_0*t) + \frac{F_0}{m}\frac{cos(\omega*t)}{\omega_0^2-\omega^2} I am to determine the initial conditions such that the undamped oscillator begins steady...
  31. N

    What's the difference between initial conditions and boundary conditions?

    As the thread title says: What's the difference between initial conditions and boundary conditions? Thanks in advance for helpful replies. :)
  32. M

    How Do You Apply Boundary Conditions to Solve a Separable PDE in a Strip?

    I need to find all the separated solns of x^2 \frac{\partial^2 u}{\partial x^2} + x\frac{\partial u}{\partial x} + \frac{\partial^2 u}{\partial y^2} = 0 in the strip {(x,y) : 0 < y < a, -\infty < x < \infty } the separated solns must also satisfy u = 0 on both the edges, that is, on...
  33. A

    Question Regarding Initial Conditions.

    I was doing a question which involved using euler's method to numerically integrate the equation dy/dt=2ty^2 in the interval [0,1], with h=0.2 but no initial conditions were given. How do I find them. I know it's something simple but I can't get it. Thanks
Back
Top