scholarly journals COMBINED EXPLICIT AND IMPLICIT METHODS FOR TIME INTEGRATION IN PARTIAL DIFFERENTIAL EQUATIONS

2018 ◽  
Author(s):  
Antonio M. Zarzur ◽  
Haroldo F. de Campos Velho ◽  
Saulo R. Freitas ◽  
Stephan Stephany
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Integration ◽  
Implicit Methods ◽  
Partial Differential

scholarly journals Using Partial Differential Equations for Pricing of Goods and Services

2016 ◽  
Vol 63 (2) ◽  
pp. 291-298 ◽  
Author(s):  
Metodi Traykov ◽  
Miglena Trencheva ◽  
Radoslav Mavrevski ◽  
Anton Stoilov ◽  
Ivan Trenchev
Keyword(s):  
Comparative Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Present Formulation ◽  
European Option ◽  
Implicit Methods ◽  
Partial Differential ◽  
Goods And Services ◽  
Black Scholes Model ◽  
Black Scholes

This article is based on the methodology of comparative analysis, using an innovative approach for pricing of various goods and services. Benchmarking is the continuous search to find and adapt better pricing methods that leading to increased profits. We will consider the numerical solution of partial differential equations, based on Black-Scholes model for pricing of goods and services within European option. Also, we will present formulation and numerical behavior of explicit and implicit methods that can be use in pricing for company assets within European option.

scholarly journals Efficient Time Integration of Nonlinear Partial Differential Equations by Means of Rosenbrock Methods

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1970
Author(s):  
Isaías Alonso-Mallo ◽  
Begoña Cano
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Method Of Lines ◽  
Time Integration ◽  
Order Reduction ◽  
Linear Case ◽  
Boundary Values ◽  
Partial Differential ◽  
Rosenbrock Methods

We avoid as as much as possible the order reduction of Rosenbrock methods when they are applied to nonlinear partial differential equations by means of a similar technique to the one used previously by us for the linear case. For this we use a suitable choice of boundary values for the internal stages. The main difference from the linear case comes from the difficulty to calculate those boundary values exactly in terms of data. In any case, the implementation is cheap and simple since, at each stage, just some additional terms concerning those boundary values and not the whole grid must be added to what would be the standard method of lines.

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