This is one of the first mathematical subdivisions at the Institute. The departmnet was set up in 1967. The first scientific investigation in the area of numerical analysis were commenced in 1965.

The key research trend in numerical analysis at the Institute is numerical methods for solving of nonlinear differential equations. The history of first systematic investigations of the methods for solving differential equations began with the consideration of second order quasilinear elliptic equations. The finite difference method has been proved for solving these differential equations. Later on the results have been generalized in two directions: in the construction and investigation of high-order accuracy difference schemes as well as in the extension of a class of equations, rejecting the usual restriction for the equation to be uniformly elliptic. Still later numerical methods for solving nonlinear elliptic equations with the nonlocal condition have been investigated.

Staff of the department (from left to right) - first row: V.Pakalnyte, L.Lapkauskaite, D.Sukvietiene, G.Kairyte, A.Valiuliene, M.Vitkauskiene, O.Stikoniene; second row: R.Siugzdaite, S.Norvaisas, R.Ciegis, M.Sapagovas, F.Ivanauskas, T.Seibakas, R.Skirmantas, A.Stikonas; baby – Viktorija Stikonas

The methods of solution of differential equations were always closely connected with the application of these equations in solving practical problems. Almost a decade ago the methods for solving systems of nonstationary differential equations describing the problems in nonlinear optics, as well as the problems of laser technology, have been started to consider. Following this course we have obtained a lot of interesting results most distinquishing of which are a stability according to boundary conditions and the principles of forming adaptive schemes.

Among other results we ought to note the substantiation of the methods for solving the equation of minimal surface, solving nonlinear problems by the Monte-Carlo method, hydrodynamics and hydrostatics problems of small volume, the methods for solving gas dynamics equations, a wide class of ecological problems, wave-quide parameter optimization problems.

A great and constant attention is paid to software at the department. Many programs have been developed to solve differential equations of various classes, a special language has been written for solving of differential equations.

Several international workshops and conferences on the methods of solution of differential equations and mathematical modelling have been organized by the effort of the department.

Staff:

Prof., Dr.habil. Mifodijus SAPAGOVAS, head of department , director of the Institute
Prof. Dr. Feliksas IVANAUSKAS, principal research fellow
Gene KAIRYTE, researcher
Dr. Vytautas KLEIZA, senior research fellow
Dr. Saulius NORVAISAS, research fellow
Violeta PAKENIENE, assistant
Dr. Rimantas SKIRMANTAS, senior researcher
Roma SIUGZDAITE, doctoral student
Dr. Arturas STIKONAS, research fellow
Olga STIKONIENE, doctoral student
Dalia SUKVIETIENE, software engineer
Aldona VALIULIENE, researcher
Marija VITKAUSKIENE, software engineer

Contact person:
            Prof., Dr.habil. Mifodijus Sapagovas
            Head of Numeric Analysis Department

Address:
            Numeric Analysis Department
            Institute of Mathematics and Informatics
            Akademijos 4, Vilnius 2600, Lithuania