Advances in Numerical Methods for Complex Models

The field of numerical methods is witnessing significant developments in tackling complex models, particularly in the areas of nonlinear distributed delay Sobolev models, fractional Laplacian, and partial integro-differential equations. Researchers are proposing innovative numerical approaches that offer improved stability, accuracy, and efficiency. Notably, the use of non-standard bases in Finite Element methods and the development of tailored discretization techniques for non-local integral terms are showing promising results. These advancements have the potential to impact various applications, including option pricing and power plant management. Noteworthy papers include: The paper on Finite Elements with weighted bases for the fractional Laplacian, which presents a novel approach achieving higher convergence rates. The paper on Numerical methods for solving PIDEs arising in swing option pricing, which proposes second-order numerical methods for convection-dominated equations with nonlocal integral terms.

Sources

An unconditionally stable numerical approach for solving a nonlinear distributed delay Sobolev model

Accuracy and stability of the hyperbolic model time integration scheme revisited

Finite Elements with weighted bases for the fractional Laplacian

Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps

Gas Fire Power Plant Management Through Numerical Approximation of Spark Spread Options

Numerical valuation of European options under two-asset infinite-activity exponential L\'evy models

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