The numerical solution of initial value problems in differential equations underpins scientific computing and modelling across disciplines. Methods can be broadly categorised into one‐step schemes, ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Numerical solution of differential and integral equations encompasses a spectrum of discretisation and approximation strategies to tackle problems that resist closed-form analysis. For ordinary and ...

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

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

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 ...

Across modern data-intensive disciplines, the union of numerical computation, statistics, and machine learning has become ...