Solve initial value problem
[DOC File]Ordinary Differential Equations
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A differential equation together with an initial condition is called . an initial value problem. The initial condition is used to determine the value of the arbitrary constant c. Example 9 = 2x, y (2) = 1. The general solution is y = + c and from the initial condition y (2) = 4 + c = 1 ( c = ( 3.
[DOC File]Numerical Solution of Initial-Value Problems
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Suppose we want to solve the following problem from t = 0 to t = 10, = ( y1, y1(0) = 1.5. The stable step size with Euler’s method is limited by (t ( 2, therefore at least = 5 time steps are necessary to integrate to t = 10. The analytical solution for this equation is y1 = 1.5e-t = 1.5e-10. Now if we want to solve the following equation ...
[DOC File]Application of First-order Differential Equations to Real ...
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The drug level immediately begins to decay. To find its mathematical expression we solve the initial-value problem: y(T)=y0(1+e-kT) Solving this initial value problem we get. y=y0(1+e-kT)e-k(t-T) This equation gives the drug level for t>T. The third dose of y0 is to be taken at t=2T and the drug just before this dose is taken is given by
[DOC File]Boundary-Value Problems
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For an nth-order equation, n conditions are required. If all the conditions are specified at the same value of the independent variable, we have an initial-value problem. If the conditions are known at different values of the independent variable, usually at the extreme points or boundaries of a system, we have a boundary-value problem.
[DOC File]Initial Value Problems - CAE Users
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Solve this system using a value of r=17 and any initial values of the dependent variables that you would like. Compare to the solution for r=26 using the same initial values. Second-order equations. To solve second order equations, we convert them to a system of two first order equations and then solve as described above. Suppose we want to solve:
[DOC File]charactarictic equation in
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Solve the nonhomogeneous system . X'=AX+, where A= (b) Solve the nonhomogeneous system . X'=AX+. A= Solve the initial-value problem . X'=AX+, A= , X(0) = Solution (a) Xc= ((t)C is the solution of X'=X. Following the method of Section 8.3 we find that . Xc= c1et +c2e-t. To find Xp we compute the inverse of the fundamental matrix ( = The inverse ...
[DOC File]MATLAB HOMEWORK 1 - nusoy
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Recall that an initial value problem consists of a differential equation along with an initial condition. Write out the initial value problem which we must solve here. (We already have the differential equation, so this means you need to find the appropriate initial condition.) (b) To simulate the conditions in the fridge we must pick the ...
[DOC File]Lehi City - Lehi City
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Try to use Taylor Series Method to solve this initial value problem: Runge-Kutta Methods. Basically, what we do for Taylor Series Method is the following: Noticed that this involves the partial derivative of which may not so easy to get. We try to express in terms of directly. Since , then , so ,
[DOC File]Calculus 3 Lecture Notes, Section 15.1
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initial condition. We call the combination of a differential equation with an initial condition an . initial value problem (IVP). The upshot of solving an IVP is that we must solve for a single number for the constant of integration in order to satisfy the initial condition. Practice: Solve the initial value problem …
[DOC File]Indefinite Integrals Calculus
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This characterization of the basic situation for which integration applies gives rise to a set of equations that will be the focus of the Lesson on The Initial Value Problem. Example 4: Solve the general differential equation . Solution: We solve the equation by integrating the …
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