Computing eigenvalues and Fučik-spectrum of the radially symmetric p-Laplacian

• Published in: Journal of computational and applied mathematics Vol. 148; no. 1; pp. 183 - 211
• Main Authors: Brown, B.M., Reichel, W.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01-11-2002; Elsevier
• Subjects: Exact sciences and technology; Mathematical analysis; Mathematics; Partial differential equations; Sciences and techniques of general use; Sturm Liouville problem; Singularity; Smoothing methods; Error analysis; Eigenfunction; Partial differential equation; Numerical approximation; Predictor corrector method; Fucik spectrum; P laplacian; Applied mathematics; Approximation error; Numerical simulation; Eigenvalue problem; Generalized sine function; Newton method; Regularity
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(02)00581-2

Eigenvalue problems for the radially symmetric p-Laplacian are discussed. We present algorithms which compute a given number of eigenvalues and Fučik-curves together with the corresponding eigenfunctions. The second-order p-Laplacian equation is transformed into a first-order system by a generalized Prüfer-transformation. To the first-order system we apply shooting algorithms, Newton's method and in case of the Fučik-curves a predictor–corrector method. Our approach requires analytical and numerical treatment of generalized sine-functions. Singular as well as regular problems are treated, and a detailed error analysis for the approximation of singular problems by regular ones are given. Numerical results are presented.