Initial conditions Definition and 133 Threads

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.

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  1. U

    Why heat PDE solution does not fully satisfy initial conditions?

    Hi, I am solving heat equation with internal heat sources both numerically and analytically. My graphs are nearly identical but! analytical one have problem at the beginning and at the end for my domain. Many people have used the same technique to solve it analytically and they got good answers...
  2. Z

    Mathematica Mathematica bug? (Solving PDEs when the initial conditions contain a derivative)

    hello I own mathematica 10.02 it is virtually impossible to solve PDE's ,even with NDSolve,if the initial conditions contain a derivative I write Derivative[1,0] [0,x] == f[x] I mean the first t derivative of u[t,x] for x at t=0 is f[x] I own a book based on Mathematica 10.3 Even if a...
  3. A

    Solving a first order differential equation with initial conditions

    Hello! Consider this ODE; $$ x' = sin(t) (x+2) $$ with initial conditions x(0) = 1; Now I've solved it and according to wolfram alpha it is correct (I got the homogenous and the particular solution) $$ x = c * e^{-cos(t)} -2 $$ and now I wanted to plug in the initial conditions and this is...
  4. MechEEE

    Transfer function with initial conditions (DE)

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  5. Safinaz

    B How to make this integral with initial conditions

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  6. VexCarido

    Runge-Kutta Projectile Approximation From Initial Conditions

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  7. S

    I Laws of physics from initial conditions?

    Are there any models, theories or physicists who propose that the fundamental laws of nature come from the initial conditions? Are there any physicists who propose that the most fundamental laws of physics emerged from initial conditions at the origin of the universe? And according to this view...
  8. A

    I Non-linear ODE: initial conditions

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  9. jisbon

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  10. Joa

    A How to Find Initial Conditions for a Fifth Order ODE in Visco-Elastic Models?

    Hello, I am trying to solve a differential equation corresponding to a visco-elastic material model consisting of 5 units of springs and dashpots connected in parallel as can be seen in the image below. I am able to come-up with a single fifth order ODE, however I am struggling to find the...
  11. Quantum Alchemy

    B How constrained are the initial conditions of the universe?

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  12. Like Tony Stark

    Initial conditions in simple harmonic motion

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  13. C

    Engineering Advanced Circuits, Laplace Transform, Find Initial Conditions

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  14. Mr Davis 97

    Find which initial conditions lead to convergence

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  15. M

    MHB Romeo and Juliet initial conditions

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  16. S

    A What are typical initial conditions for the Schrödinger eq?

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  17. S

    I Can initial conditions for an ODE be given by functions instead of constants?

    Hi, I am trying to solve an ODE, however, the initial conditions are not known. From PDE examples, which are quite different, I see that some examples have initial conditions given by functions, and not by constants, i.e:: y(0) = x^2 I may have not modeled the problem correctly yet, however, I...
  18. A

    Why Set the Inner Boundary Condition to -1 in Radial Flow Equations?

    Hello gents, Q:/ what is the reason for letting the inner boundary condition = (-1) when solving the radial flow of infinite form of diffusivity equation, and i would like to know what will happened if i didn't equate it with (-1). as in the attached pic: https://i.imgur.com/AVesmHM.png
  19. A

    Supressed harmonics with certain initial conditions

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  20. karush

    MHB -17.2.53 Find the unique solution from initial conditions.

    the function y_p is a particular solution to the specified nonhomogeneous equation. Find the unique solution satisfying the equation and the given initial conditions. $y'' + 7y' = 7x$ $y_p=\frac{1}{2}x^2-\frac{1}{7}x$ $y(0)=y'(0)=0$ $r^2+7r=0$ $r=0$ $r=-7$
  21. Vincent Isoz

    Self Buckling Initial conditions

    Hi For a book I'm writing, i try to write a very very very detail proof of self-buckling. I did it almost by taking inspiration of: https://en.wikipedia.org/wiki/Self-buckling But i really really don't get how we arrive to, that when, x=0 as we obviously must have: \dfrac{\mathrm{d}^2...
  22. K

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  23. mattyboson12

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  24. Mr Davis 97

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  25. kostoglotov

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  26. Yukterez

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  27. V

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  28. M

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  29. W

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  30. ognik

    MHB Help with ODE initial conditions

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  31. T

    Solving a PDE w/ given boundary and initial conditions

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  32. C

    Truss Free Body Diagram & initial conditions

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  33. T

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  34. G

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  35. Zafa Pi

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  36. J

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  37. S

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  38. A

    Simple Harmonic Motion, Initial Displacement vs Initial Cond

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  39. B

    Determine initial conditions of the capacitor's Vc and inductor's Il at t=0

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  40. E

    Material Model: initial conditions of equation?

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  41. C

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  42. WannabeNewton

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  43. A

    Partial Differential Equation with initial conditions

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  44. M

    A question about uniqueness of initial conditions

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  45. Y

    MHB Solve Recurrence Relation w/ 3 Terms & Initial Conditions

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  46. D

    Engineering Solving RL Circuit Differential Equation: Initial Conditions

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  47. Z

    Burgers Equation Question - cannot satisfy initial conditions

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  48. J

    How is the initial conditions for PDE?

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  49. L

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  50. I

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