We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro‐differential equations.
- Authors
Dzhumabaev, Dulat
- Abstract
The article presents a new general solution to a loaded differential equation and describes its properties. Solving a linear boundary value problem for loaded differential equation is reduced to the solving a system of linear algebraic equations with respect to the arbitrary vectors of general solution introduced. The system's coefficients and right sides are computed by solving the Cauchy problems for ordinary differential equations. Algorithms of constructing a new general solution and solving a linear boundary value problem for loaded differential equation are offered. Linear boundary value problem for the Fredholm integro‐differential equation is approximated by the linear boundary value problem for loaded differential equation. A mutual relationship between the qualitative properties of original and approximate problems is obtained, and the estimates for differences between their solutions are given. The paper proposes numerical and approximate methods of solving a linear boundary value problem for the Fredholm integro‐differential equation and examines their convergence, stability, and accuracy.
- Subjects
LINEAR algebra; NUMERICAL solutions to boundary value problems; DIFFERENTIAL equations; NUMERICAL solutions to integro-differential equations; BOUNDARY value problems
- Publication
Mathematical Methods in the Applied Sciences, 2018, Vol 41, Issue 4, p1439
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4674