An iterative method for solving an exact initial value problem of the second order by a hybrid computerMany problems of engineering are described only by great non-linear systems of differential equations. Their equations often have a similar structure. Usually such problems cannot be solved by an...
Let the IVPx˙(t)=f(t,x(t)),t∈[t0,tf],x(t0)=x0, where f(t,x(t))∈Rn, t∈[t0,tf], satisfies the necessary conditions under which the problem has a unique solution. In this section an algorithm is presented which solves IVPs for ODEs by means of a BDF approach [8, Chap...
Find {eq}f {/eq} by solving the initial-value problem. {eq}f'(x) = 9x^2 + 6x - 3 {/eq}; {eq}\quad f(2) = 6 {/eq} Initial Value Problem: First, we integrate both sides of the given differential equation (if variables are isolated from each other) to de...
thus doubling the number of real variables, and hence we work in 4+2 dimensions:\(x_1\),\(x_2\),\(y_1\),\(y_2\)and\(t_1\),\(t_2\). In this paper we solve the initial value problem of the 3-wave
Bound to specific constraints, the method returns an approximate solution assuredly within a given tolerance provided by a user. This makes it different from a large variety of single- and multi-step methods for solving initial value problems that provide results up to some undefined error in the...
Comparative to the results obtained using EpODE [9], a specialized numerical software for ODEs, in our case an acceptable efficiency level can be obtained for smaller problems due to the fact that Ts and Tp are greater in the case of using a CAS. The limit on problem dimension which can ...
Find f(x) by solving the initial value problem: f′(x)=2x+3ex+x2;f(1)=3. Initial Value Problems: An initial value problem, often abbreviated IVP, is any problem where we have a derivative and some particular value for the function, called the initial value...
Since the shortest paths do not provide the unique solution on triangle meshes, we solve the initial value problem in an indirect manner: given a fixed point and an initial tangent direction on a triangle mesh M, we first compute a geodesic curve (gamma) over cap on a piecewise smooth ...
Baker J. and Puzio R.: New Method for Solving the Initial Value Problem with Application to Multiple Black Holes, Phys. Rev. D 59, 04 4030 (1999)J Baker and R Puzio. New Method for Solving the Initial Value Problem with Application to Multiple Black Holes. Phys. Rev. D 59 04 4030,...
Conventional Numerical Methods for Solving the Initial Value Problem Book Title Numerical Solutions of the N-Body Problem Pages pp 3-48 Copyright 1985 DOI 10.1007/978-94-009-5412-0_2 Print ISBN 978-94-010-8889-3 Online ISBN 978-94-009-5412-0 Series Title Mathematics and Its Applications ...