Ukhan'ov O. FD-method for Sturm-Liouville problems. Exponential rate of convergence.

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0499U003080

Thesis Registration Form

0499U003080.pdf

Applicant for

Specialization

  • 01.01.07 - Обчислювальна математика

22-10-1999

Specialized Academic Board

Д 26.194.01

Essay

The function-discrete method for solving Sturm-Liouville problem with boundary value conditions of third kind, periodic and anti-periodic conditions is analyzed in thesis. Sufficient conditions are found which guarantee convergence rate of method to be not slower than convergence rate of geometric progression with denominator, which depends directly proportionally on discretization parameter and inversely proportionally on ordinal number of corresponding eigen value. The generalization of classic asymptotic expansions for eigen values and eigen functions of Sturm-Liouville problem with non-smooth coefficient in differential equation, taken in Liouville form, is obtained.

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