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- Title
Convergence Rate of the Galërkin Method for Boundary Value Problem for Mixed-Type Operator-Differential Equations.
- Authors
Ahmed, Abdel Baset I.
- Abstract
The paper studies the BVP for a mixed-type firstorder linear operator-differential equations. We prove that there exists an absolutely continuous-unique solution in a certain Sobolev-type space ẘ (H,H1). We provide the Galërkin method for sufficiently smooth selfadjoint positively definite operator Φ(t) and α-subordinate differentiable operator S(t), 0 ≤ α < 1. The investigated method depends on a special basis {ei}∞ i =1 of the operator Ψ similar to Φ. Moreover, using the eigenvalues λi of the operator Ψ to derive the error estimates of the approximate solutions. Through this work, we investigate how quickly the approximate solutions approach to the exact one.
- Subjects
BOUNDARY value problems; DIFFERENTIAL-difference equations; EQUATIONS; LINEAR equations; SELFADJOINT operators
- Publication
IAENG International Journal of Applied Mathematics, 2021, Vol 51, Issue 4, p984
- ISSN
1992-9978
- Publication type
Article