IEEE

Linear Operator Differential Equations with Applications to Linear Time-Varying Systems

Abstract: A classical result in linear system theory is that a causal linear time-varying (LTV) system has a smooth finite dimensional realization if and only if its impulse response exhibits a ...
Scientific Research Publishing

Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method ()

The object of this work is to describe how to implement the differential ‎transformation method (DTM) for finding exact and approximate solutions of ‎the second-order random differential equations. To ...
Scientific Research Publishing

Cyclic Operator Decomposition for Solving the Differential Equations ()

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator ...
JSTOR Daily

OPERATOR SPLITTING FOR PARTIAL DIFFERENTIAL EQUATIONS WITH BURGERS NONLINEARITY

We provide a new analytical approach to operator splitting for equations of the type u t = Au + uu x where A is a linear differential operator such that the equation is well-posed. Particular examples ...
lse

Partial Differential Equations

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in ...
marktechpost

Newton Informed Neural Operator: A Novel Machine Learning Approach for Computing Multiple Solutions of Nonlinear Partials Differential Equations

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...