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View article: On Non-Linear Differential Systems with Mixed Boundary Conditions
On Non-Linear Differential Systems with Mixed Boundary Conditions Open
For the constructive analysis of locally Lipschitzian system of non-linear differential equations with mixed periodic and two-point non-linear boundary conditions, a numerical-analytic approach is developed, which allows one to study the s…
View article: On the jump control problem for boundary-value problems with state-dependent impulses
On the jump control problem for boundary-value problems with state-dependent impulses Open
UDC 517.9 We show how an appropriate parametrization technique and special successive approximations can help to control unknown jumps in the case of nonlinear boundary-value problems with state-dependent impulses. The practical applicatio…
View article: Lower bounds on par with upper bounds for few-electron atomic energies
Lower bounds on par with upper bounds for few-electron atomic energies Open
The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this pape…
View article: Comparison of an improved self-consistent lower bound theory with Lehmann’s method for low-lying eigenvalues
Comparison of an improved self-consistent lower bound theory with Lehmann’s method for low-lying eigenvalues Open
Ritz eigenvalues only provide upper bounds for the energy levels, while obtaining lower bounds requires at least the calculation of the variances associated with these eigenvalues. The well-known Weinstein and Temple lower bounds based on …
View article: Lower Bounds for Nonrelativistic Atomic Energies
Lower Bounds for Nonrelativistic Atomic Energies Open
A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, L…
View article: Comparison of an Improved Self-consistent Lower Bound Theory with Lehmann’s Method for Low-lying Eigenvalues
Comparison of an Improved Self-consistent Lower Bound Theory with Lehmann’s Method for Low-lying Eigenvalues Open
Ritz eigenvalues only provide upper bounds for the energy levels, while obtaining lower bounds requires at least the calculation of the variances associated with these eigenvalues. The well-known Weinstein and Temple lower bounds based on …
View article: Upper and lower bounds for tunneling splittings in a symmetric double-well potential
Upper and lower bounds for tunneling splittings in a symmetric double-well potential Open
Ground state tunneling gaps: solid circles are mean of eigenvalues and lower bound gaps.
View article: The seventh international Workshop - 2018 "Constructive methods for non-linear boundary value problems"
The seventh international Workshop - 2018 "Constructive methods for non-linear boundary value problems" Open
Constructive Methods for Non-Linear Boundary Value Problems had taken place in Miskolc, Hungary.The list of participants and the program can be found on the workshop web site: http://mat76.mat.
View article: Parametrisation for boundary value problems with transcendental non-linearities using polynomial interpolation
Parametrisation for boundary value problems with transcendental non-linearities using polynomial interpolation Open
A constructive technique of analysis involving parametrisation and polynomial interpolation is suggested for general non-local problems for ordinary differential systems with locally Lipschitzian transcendental non-linearities. The practic…
View article: On boundary value problems with prescribed number of zeroes of solutions
On boundary value problems with prescribed number of zeroes of solutions Open
We show how appropriate parametrisation technique and successive approximations can help to investigate solutions of Emden-Fowler type equations with a given number of zeroes.The technique can be efficiently applied for more general equati…
View article: A two-layer approach to the coupled coherent states method
A two-layer approach to the coupled coherent states method Open
In this paper, a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamic…
View article: On non-linear boundary value problems and parametrisation at multiple nodes
On non-linear boundary value problems and parametrisation at multiple nodes Open
We show how a suitable interval division and parametrisation technique can help to essentially improve the convergence conditions of the successive approximations for solutions of systems of non-linear ordinary differential equations under…