A novel analytical operator method to solve linear ordinary differential equations with variable coefficients

2009/02/05 by Wrick Sengupta, Sengupta, Wrick
Mathematics · #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.0902.0910

openalex publication_date 2009/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series solution is obtained without having to calculate series coefficients by recurrence relation.Both homogeneous and inhomogeneous equations are solved identically without having to calculate the Green's function explicitly in the case of inhomogeneous equation.Closed-form solutions are obtained for all the special functions appearing in mathematical physics. For a second-order equation both the independent solutions are obtained without invoking Wronskians, even when the indices differ by an integer.

Citations

• On Adomian's Decomposition Method for Solving Differential Equations

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