Construction and computation of variable coefficient Sylvester differential problems. (English) Zbl 0864.65046
Summary: Initial value problems for Sylvester differential equations \(X'(t)= A(t)X(t)+ X(t) B(t) +F(t)\) with analytic matrix coefficients are considered. First, an exact series solution of the problem is obtained. Given a bounded domain \(\Omega\) and an admissible error \(\varepsilon\), a finite analytic-numerical series solution is constructed, so that the error with respect to the exact series solution is uniformly upper bounded by \(\varepsilon\) in \(\Omega\). An iterative procedure for the construction of the approximate solutions is included.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A30 | Linear ordinary differential equations and systems |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
variable coefficient; Sylvester differential equation; initial value problem; Frobenius method; Gronwall’s inequality; error bound; numerical series solutionReferences:
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