Nature

Error Analysis and Numerical Methods for Parabolic Partial Differential Equations

Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...
JSTOR Daily

Studies on Error Propagation for Certain Nonlinear Approximations to Hyperbolic Equations: Discontinuities in Derivatives

SIAM Journal on Numerical Analysis, Vol. 31, No. 3 (Jun., 1994), pp. 655-679 (25 pages) The accuracy of numerical approximations to piecewise smooth solutions of hyperbolic partial differential ...
JSTOR Daily

NUMERICAL APPROXIMATION OF SEMILINEAR SUBDIFFUSION EQUATIONS WITH NONSMOOTH INITIAL DATA

We consider the numerical approximation of a semilinear fractional order evolution equation involving a Caputo derivative in time of order α ϵ (0,1). Assuming a Lipschitz continuous nonlinear source ...
Nature

Backward Stochastic Differential Equations and Numerical Methods

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...