Five Ways of Reducing the Crank-Nicolson Oscillations

Crank-Nicolson is a popular method for solving parabolic equations because it is unconditionally stable and second order accurate. One drawback of CN is that it responds to jump discontinuities in the initial conditions with oscillations which are weakly damped and therefore may persist for a long time. We present a selection of methods to reduce the amplitude of these oscillations

Numerical Solution of Parabolic Equations

These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory.Among the special features of this book can be mentioned the presentation of a practical approach to reliable estimates of the global error, including warning signals if the reliability is questionable. The technique is generally applicable for estimating the discretization error in numerical approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal expense.Problems in two space dimensions are effectively handled using the Alternating Direction Implicit (ADI) technique. We present a systematic way of incorporating inhomogeneous terms and derivative boundary conditions in ADI methods as well as mixed derivative terms

Searching for a Space for Conversation: A study on how environment affects the articulation of the art experience among opera audiences at The Royal Danish Theatre

“Tell me about your experience in the theatre today”. Even though theatres (with this question) may seek honest, personal, and in depth answers from the audience, this question often results in superficial responds focused on what the audience suspect the theatre wants to hear. It can thus be difficult to get personal and detailed knowledge about the audiences’ experience. In a time, where theatres with different means (co-creation, participation etc.) try to keep audience loyal and engaged, this knowledge is important. In our project, we explore how different situations, locations, questions etc. affect conversations about art experiences and in this article we describe our “search for a space for conversation”. We explore how the space affects the conversation, and how the setting can emphasize certain elements. What happens to the conversation if we sit around an ordinary meeting table, if we walk and talk outside the art institution or if we talk inside the auditorium, where we had the original art experience? This explorative study is part of the project “A Suitcase of Methods”, which is housed by The Royal Danish Theatre and financially supported by The Bikuben Foundation