Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

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 ...

Differential equations don’t have to feel like an endless maze of formulas. With the right mix of tech tools, real-world context, and problem-solving strategies, they can become a skill you actually ...

In this paper, we consider the valuation of European and path-dependent options in foreign exchange markets when the currency exchange rate evolves according to the Heston model combined with the ...

In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions to nonlinear differential equations used to model turbulence.

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

Integral equations in various scientific theories and their relation to differential equations. Methods of solving linear problems with Hilbert Schmidt, Cauchy, and Wiener-Hopf type kernels; ...