## Constructive solution of coupled second order delay differential equations with variable coefficients.(English)Zbl 0878.34057

Summary: We study initial value problems for coupled order delay differential equations with variable coefficients. By means of the application of the method of steps and the method of Frobenius, the exact solution of the problem is constructed. Then, in a bounded domain, a finite analytic solution with error bounds is provided. Given an admissible error $$\varepsilon$$, we give the number of terms to be taken in the infinite series exact solution so that the approximation error be smaller than $$\varepsilon$$ in the bounded domain.

### MSC:

 34K05 General theory of functional-differential equations 65Q05 Numerical methods for functional equations (MSC2000) 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A05 Explicit solutions, first integrals of ordinary differential equations 65G99 Error analysis and interval analysis
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