• CSC466/2305: Numerical Methods for Optimization Problems, TU 15-17, TR 15-16

• CSC336: Numerical Methods, TU: 18:00-21:00
• CSC2321: Matrix Calculations, WE: 14:00-16:00

• CSC336: Numerical Methods

• CSC456-2306: High-Performance Scientific Computing, TU: 13:00-15:00; TH: 14:00-15:00
  Note: Registration for non-CS grad students to CSC2306 will open on August 23rd.
• CSC436: Numerical Algorithms, WE: 13:00-15:00; FR: 13:00-14:00

• CSC2321: Matrix Calculations
• CSC336: Numerical Methods

• CSC336: Numerical Methods

• CSC456-2306: High-Performance Scientific Computing
• CSC336: Numerical Methods
  I expect that both courses will be offered in-person and online (synchronously and asynchronously)
  Update 20 Nov 2020: Both courses will be offered online (synchronously and asynchronously)

• CSC436: Numerical Algorithms
  offered in-person and online (synchronously and asynchronously)

Selected Publications

• A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing, Dawei Wang, Kirill Serkh, and Christina Christara
• Bilateral XVA pricing under stochastic default intensity: PDE modelling and computation, Yuwei Chen and Christina Christara
• Penalty and Penalty-Like Methods for Nonlinear HJB PDEs, Christina Christara and Ruining Wu
• Penalty Methods for Bilateral XVA Pricing, in European and American Contingent Claims by a PDE Model, Yuwei Chen and Christina Christara
• Analysis of quantization error in financial pricing via finite difference methods, Christina C. Christara and Nat Chun-Ho Leung
• Partial Differential Equation pricing of contingent claims under stochastic correlation, Nat Chun-Ho Leung, Christina C. Christara and Duy-Minh Dang
• Spread option pricing using ADI methods, Vida Heidarpour-Dehkordi and Christina C. Christara
• PDE option pricing with variable correlations, Christina C. Christara and Nat Chun-Ho Leung
• Option pricing in jump diffusion models with quadratic spline collocation, Christina C. Christara and Nat Chun-Ho Leung
• An efficient numerical PDE approach for pricing foreign exchange interest rate hybrid derivatives, Duy Minh Dang, Christina C. Christara, Kenneth R. Jackson and Asif Lakhany
• Graphics processing unit pricing of exotic cross-currency interest rate derivatives with a foreign exchange volatility skew model, Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson
• A Highly Efficient Implementation on GPU Clusters of PDE-Based Pricing Methods for Path-Dependent Foreign Exchange Interest Rate Derivatives, Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson
• An Efficient GPU-Based Parallel Algorithm for Pricing Multi-Asset American Options, Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson
• Adaptive and high-order methods for valuing American options, Christina C. Christara and Duy Minh Dang
• A Parallel Implementation on GPUs of ADI Finite Difference Methods for Parabolic PDEs with Applications in Finance, Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson
• A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives, Duy Minh Dang, Christina C. Christara, Kenneth R. Jackson and Asif Lakhany
• Pricing Multi-Asset American Options on Graphics Processing Units Using a PDE Approach, Duy Minh Dang, Christina C. Christara and Kenneth R. Jackson
• Quartic spline collocation for second-order boundary value problems, Christina C. Christara and Guohong Liu
• Quadratic spline collocation for one-dimensional linear parabolic partial differential equations, Christina C. Christara, Tong Chen and Duy Minh Dang
• Quartic spline collocation for fourth-order boundary value problems, Christina C. Christara, Ying Zhu and Jingrui Zhang
• A High-Performance Method for the Biharmonic Dirichlet Problem on Rectangles, Christina C. Christara and Jingrui Zhang
• Optimal Quadratic and Cubic Spline Collocation on Nonuniform Partitions, Christina C. Christara, and Kit Sun Ng
• Adaptive Techniques for Spline Collocation, Christina C. Christara, and Kit Sun Ng
• GIA-induced secular variations in the Earth's long wavelength gravity field: Influence of 3-D viscosity variations (short communication), Konstantin Latychev, Jerry X. Mitrovica, Mark E. Tamisiea, Jeroen Tromp, Christina C. Christara and Robert Moucha
• Glacial isostatic adjustment on 3-D Earth models: a finite-volume formulation, Konstantin Latychev, Jerry X. Mitrovica, Jeroen Tromp, Mark E. Tamisiea, Dimitri Komatitsch, and Christina C. Christara
• Optimal Quadratic Spline Collocation on Non-Uniform Partitions, Christina C. Christara, and Kit Sun Ng
• Optimal Cubic Spline Collocation on Non-Uniform Partitions, Christina C. Christara, and Kit Sun Ng
• Quadratic Spline Galerkin Method for the Shallow Water Equations, Anita T. Layton, Christina C. Christara, and Kenneth R. Jackson
• Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations, Anita T. Layton, Christina C. Christara, and Kenneth R. Jackson
• Quadratic Spline Collocation Revisited: Extension to Systems of Elliptic PDEs, Christina C. Christara and Kit Sun Ng
• Fast Fourier Transform Solvers and Preconditioners for Quadratic Spline Collocation, Christina C. Christara and Kit Sun Ng
• An Efficient Transposition Algorithm for Distributed Memory Computers, C. Christara, X. Ding and K. R. Jackson
• Multigrid and Multilevel Methods for Quadratic Spline Collocation, Christina C. Christara and Barry Smith
• Parallel solvers for spline collocation equations, C. C. Christara
• Quadratic spline collocation methods for elliptic partial differential equations, C. C. Christara
• High performance computing of elliptic partial differential equations with spline collocation, C. C. Christara
• Parallel computation of partial differential equations on distributed memory machines, C. C. Christara
• Multicolour orderings and iterative methods for elliptic equations, C. C. Christara
• Domain decomposition and incomplete factorisation methods for partial differential equations, C. C. Christara
• Schur complement preconditioned conjugate gradient methods for spline collocation equations, C. C. Christara
• Conjugate gradient methods for spline collocation equations, C. C. Christara
• A Domain Decomposition Spline Collocation Method for Elliptic Partial Differential Equations, C. C. Christara and E. N. Houstis
• A Parallel Spline Collocation - Capacitance Method for Elliptic Partial Differential Equations, C. C. Christara, E. N. Houstis and J. R. Rice
• Geometry Decomposition based Methods for solving Elliptic Partial Differential Equations, C. C. Christara, A. Hadjidimos, E. N. Houstis, J. R. Rice and E. A. Vavalis
• Quadratic Spline Collocation Methods for two point boundary value problems, E. N. Houstis, C. C. Christara and J. R. Rice
• Performance of Scientific Software, E. N. Houstis, J. R. Rice, C. C. Christara and E. A. Vavalis
• Scientific Computing by Numerical Methods, C. C. Christara and K. R. Jackson

Supervised students' theses

• High-order numerical methods for parabolic PDEs with nonsmooth data: a perspective from option pricing, Dawei Wang, Ph.D. thesis, University of Toronto, June 2024, 124 pages.
• Numerical PDE Methods for Pricing Bilateral XVA, Yuwei Chen, Ph.D. thesis, University of Toronto, February 2023, 123 pages.
• Penalty Methods for Nonlinear Problems in Financial Option Pricing, Ruining (Ray) Wu, MSc Research Paper, February 2021, 121 pages.
• Numerical Methods for Pricing Multi-Asset Options, Yuwei Chen, M.Sc. thesis, University of Toronto, January 2018, 75 pages.
• ``PDE option pricing: analysis and application to stochastic correlation'', Nat Chun-Ho Leung, Ph.D. thesis, University of Toronto, June 2017, 119 pages.
• ``Efficient and accurate numerical PDE methods for pricing financial derivatives'', Mufan (Bill) Li, B.A.Sc. thesis, University of Toronto, April 2015, 35 pages.
• ``Modeling multi-factor financial derivatives by a Partial Differential Equation approach with efficient implementation on Graphics Processing Units'', Duy Minh Dang, Ph.D. thesis, University of Toronto, August 2011, 228 pages.
• ``A study of a discrete element method based granular dynamics solver'', Tina Yee, M.Sc. thesis, University of Toronto, September 2009, 43 pages.
• ``Multigrid and Spline Collocation Methods on Non-uniform Grids'', Guoyu Wang, M.Sc. thesis, University of Toronto, September 2008, 98 pages.
• ``Bi-quartic Spline Collocation Methods for Fourth-order Boundary Value Problems with an Application to the Biharmonic Dirichlet Problem'', Jingrui Zhang, Ph.D. thesis, University of Toronto, January 2008, 160 pages.
• Adaptive Finite Difference Methods for Valuing American Options, Duy Minh Dang, M.Sc. Thesis, University of Toronto, September 2007, 119 pages.
• Quartic Spline Collocation Methods For Second-Order Two-Point Boundary Value ODE Problems, Guohong Liu, M.Sc. Thesis
• Pricing Convertible Bonds with Dividend Protection subject to Credit Risk Using a Numerical PDE Approach, Qingkai Mo, M.Sc. Thesis
• An Efficient Algorithm Based on Quadratic Spline Collocation and Finite Difference Methods for Parabolic Partial Differential Equations, Tong Chen, M.Sc. Thesis
• Pricing Convertible Bonds using Partial Differential Equations, Lucy Xingwen Li, M.Sc. Thesis
• Spline Collocation on Adaptive Grids and Non-Rectangular Domains, Kit Sun Ng, Ph.D. Thesis
• Multigrid and Cubic Spline Collocation Methods for Advection Equations, Zheng Zeng, M.Sc. Thesis
• Towards a high-performance method for the biharmonic Dirichlet problem, Jingrui Zhang, Research Paper (equivalent to M.Sc. Thesis)
• Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems, Ying Zhu, M.Sc. Thesis
• High-Order Spatial Discretization Methods for the Shallow Water Equations, Anita W. Tam, Ph.D. Thesis, co-supervised by Ken Jackson
• Quadratic Spline Collocation Methods for Systems of Elliptic PDEs, Kit Sun Ng, M.Sc. Thesis
• Numerical Solution of the Shallow-Water Equations on Distributed Memory Systems, Xiaoliang (Lloyd) Ding, M.Sc. Thesis, co-supervised by Ken Jackson
• Fast Fourier transform solvers for quadratic spline collocation, Athanasia Constas, M.Sc. Thesis

Other publications of possible interest

• A brief introduction to MATLAB, Christina C. Christara and Winky Wai
• Tutorial on MATLAB, Christina C. Christara
• A brief introduction to MAPLE, Christina C. Christara
• Tutorial on MAPLE, Christina C. Christara
• Starting on Latex, Christina C. Christara (includes some tips on MATLAB plots)

You may also be interested in looking at the www site of the Numerical Analysis and Scientific Computing Group of the Department of Computer Science at the University of Toronto. Alternatively, you have anonymous ftp access to the respective ftp site, by connecting to ftp.cs.toronto.edu, logging in as anonymous and changing to directory na.

Contact infomation:

E-mail:	ccc SYMBOL_AT cs DOT toronto DOT edu
Telephone number:	+1 416 978 7360
Fax number:	+1 416 946 7132 or +1 416 978 1931
Office:	BA 4226, Bahen Center for Information Technology, 40 St. George Street
Mailing address:	Professor Christina Christara Department of Computer Science University of Toronto 40 St. George Street Toronto, Ontario M5S 2E4 Canada

Visiting our department?
Driving and other travel directions are available.
Some information about accommodation near the campus is also available. (May be a bit outdated.)