Reproducing kernel Hilbert space method is utilized in this paper as an efficient approach to solve singular fourth order ...

This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical ...

Compartment models have been proposed in the 1920s as a model for the spread of an infectious disease in a society, in a famous article by Kermack and ...

Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation ...

Today, computational sciences have become indispensable. The advancement of high-performance computing infrastructure has triggered new questions, and as a result, computational sciences have led to ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...