Name
Title | ||
|---|---|---|
Second-order difference approximations for Volterra equations with the completely monotonic kernels |
Abstract | ||
|---|---|---|
The second-order difference type methods are studied for the solution of the problem $$u^{prime}(t)+{{int}_{0}^{t}} (t-tau)u (tau)dtau = 0 , tu003e0, u(0) = u_{0}, $$with ( L(t)=sum limits _{j = 1}^{n} a_{j}(t) L_{j} ). The operators Lj are densely defined positive self-adjoint linear operator on a Hilbert space H and have spectral decompositions with respect to a common resolution of the identity {Eλ} in H. Here, the kernel functions aj(t), 1 ≤ j ≤ n, are completely monotonic on (0, ∞) and locally integrable, but not constant. The convergence properties of the time discretization are proven in the weighted ( l^{1}(rho ;0,infty ; mathbf {H} ) and ( l^{infty }(rho ; 0, infty ; mathbf {H} ) norm, where ρ is a given weighted function. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s11075-018-0580-5 | Numerical Algorithms |
Keywords | Field | DocType |
Integro-differential equations, Completely monotonic kernels, The second-order backward difference time-stepping schemes, Weighted l1 asymptotic convergence behavior, 45K05, 65D30, 34K30, 65L07, 65M12 | Prime (order theory),Hilbert space,Monotonic function,Combinatorics,Mathematical analysis,Operator (computer programming),Linear map,Volterra equations,Mathematics | Journal |
Volume | Issue | ISSN |
81.0 | 3 | 1572-9265 |
Citations | PageRank | References |
0 | 0.34 | 13 |
Authors | ||
1 | ||