More on Asymptotic Approximation for Matrix Differential Equations
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By means of WKB-methods, an asymptotic approximation is obtained for the solution of \(Y''=t^hA(t)Y\), where \(h\) is a real number, and \(A(t)\) a Hermitean \(n\times n\)-matrix for real \(t\), which is analytic and invertible on \((a,\infty]\). The eigenvalues \(\lambda_j\) of \(t^hA\) shall satisfy \(1+(\lambda_j')^2/(16\lambda_j^3)\neq 0\) on \((a,\infty]\). Under a modified eigenvalue condition the result is valid in the case that \(A(t)\) is meromorphic at \(t=\infty\) and not invertible there.
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), matrix differential equation, Applied Mathematics, Linear ordinary differential equations and systems, asymptotic approximation, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, WKB-methods, Analysis
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), matrix differential equation, Applied Mathematics, Linear ordinary differential equations and systems, asymptotic approximation, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, WKB-methods, Analysis
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