New Developments of Newton-Type Iterations for Solving Nonlinear Problems

Dr. Ochbadrakh Chuluunbaatar is a computational physicist with expertise in mathematical modeling, variational methods, and numerical approaches for solving few-body problems. His research focuses on high-precision calculations in quantum mechanics, particularly the energy states of helium-like atoms and ionization behavior under particle impact. Dr. Chuluunbaatar has authored or co-authored over 230 scientific publications and contributed to the development of valuable computational tools in physics.

Dr. Tugal Zhanlav is a Professor of Mathematics at the Mongolian Academy of Sciences. His research interests lie in computational mathematics, with a focus on wavelet analysis, spline approximations, numerical methods for linear algebra problems, iterative methods for solving nonlinear systems, and the convergence and stability of finite-difference schemes.

This information can be further divided into two sections:

• Education:
  • 1982: Candidate of Sciences in Physics and Mathematics (Computing Center of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia) - Thesis: "Spline Collocation Method for Parabolic Partial Differential Equations with Variable Coefficients" (Supervisor: Prof. Yu.S. Zaviyalov)
  • 1992: Doctor of Sciences in Physics and Mathematics (JINR, Dubna, Russia) - Thesis: "Generalized Continuous Analogue of Newton Method and Spline Method for Numerical Solution of Some Nonlinear Problems in Theoretical Physics" (Scientific Advisor: Prof. I.V. Puzynin)
• Research Interests:
  • Computational aspects of wavelet analysis
  • Wavelet and spline approximations
  • Numerical methods for problems of linear algebra
  • Iterative methods for solving systems of nonlinear equations
  • Convergence and stability of finite-difference schemes

Part 1. Newton-Type Iterations for Nonlinear Equations.- 1. Newton-Type Iterations, Convergence and Accelerations.- 2. Two-Sided Approximations.- 3. New Developments and Extensions of Newton-Type Methods.- 4. Derivative-Free Iterative Methods.- Part 2. Higher Order Iterations for Systems of Nonlinear Equations.- 5. Higher Order Newton-Type Iterations.- Part 3. Applications.- 6. Newton-Type Iterations for Solving Some Problems in Linear Algebra.