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methods; that is, x n+1 was ultimately only a function of x n . A disadvantage of single-step methods is that to achieve good accuracy often requires the use of higher-order methods (e.g., fourth- or fth-order Runge Kutta). But higher-order methods need many function evaluations per step, and so are computationally expensive. Implicit single-step methods, although inherently stable, are not more accurate than explicit methods, although they can track fast changes in the solution x(t) better than can explicit methods (recall Example 10.5). However, implicit methods may require nonlinear system solvers (i.e., 7 methods) as part of their implementation. This is a complication that is also not necessarily very ef cient computationally. Furthermore, the methods in 7 possess their own stability problems. Therefore, in this section we introduce multistep predictor corrector methods that overcome some of the de ciencies of the methods we have considered so far. In this section we return to consideration of a single rst-order ODE IVP x (1) (t) = dx(t) = f (x(t), t), x0 = x(0). dt (10.122)

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Call the XMLHttpRequest object s open() method to create a request by supplying the URL, the request method (POST, GET or PUT), and whether the request should be processed asynchronously (or synchronously). An example of such a call follows. In this case, the HTTP GET method is used, and the URL is getphotoinfo.jsp. This JSP is running on the server side. The JSP, hypothetically for this example, provides information on a specified photo; the data is returned in XML format and can be a structure. The ID of the photo to query is 102. With the HTTP GET method, the parameters to the request are supplied as part of the URL, after the question mark.

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92 BASIC ARCHITECTURE OF DIFFERENTIATED SERVICES Diffserv divides a network into several domains A DS domain w1x is a continuous set of nodes that operate with a common set of resource provision policies and PHB definitions It has a well-defined boundary, and so there are two types of nodes associated with a DS domain: boundary nodes and interior nodes Boundary nodes connect the DS cloud to other domains Interior nodes are connected to other interior nodes or boundary nodes, but they must be within the same DS domain The boundary nodes are assigned the duty of classifying ingress traffic so that incoming packets are marked appropriately to choose one of the PHB groups supported inside the domain They also enforce the TCAs between their own DS domain and the other domains it connects to.

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The TCA specifies the rules used to realize the service, such as metering, marking, and discarding Interior nodes map the DS codepoints of each packet into the set of PHBs and perform appropriate forwarding behavior Any non-DS-compliant node inside a DS domain results in unpredictable performance and a loss of end-to-end QoS A DS domain is generally made up of an organization s intranet or an ISP, that is, a network controlled by a single entity Diffserv is extended across domains by SLAs between them An SLA specifies rules such as traffic remarking, actions to be taken for out-of-profile traffic, etc The TCAs between domains are decided from this SLA Figure 91 shows the basic elements of a Diffserv network Depending on direction of traffic flow, DS boundary nodes can be both ingress nodes and egress nodes.

Traffic enters the DS cloud through an ingress node and exits through an egress node An ingress node is responsible for enforcing the TCA between the DS domain and the domain of the sender node An egress node shapes the outgoing traffic to make it compliant with the TCA between its own DS domain and the domain of the receiver node Flows are classified by predetermined rules so that they can fit into a limited set of class flows The boundary routers use the 8-bit type of service ToS field of the IP header, called the DS field in Diffserv terminology, to mark the packet for preferential treatment by the interior routers Six bits.

12.1 INTRODUCTION The subject of partial differential equations (PDEs) with respect to the matter of their numerical solution is impossibly large to properly cover within a single chapter (or, for that matter, even within a single textbook). Furthermore, the development of numerical methods for PDEs is a highly active area of research, and so it continues to be a challenge to decide what is truly fundamental material to cover at an introductory level. In this chapter we shall place emphasis on wave propagation problems modeled by hyperbolic PDEs (de ned in Section 12.2). We will consider especially the nite-difference time-domain (FDTD) method [8], as this appears to be gaining importance in such application areas as modeling of the scattering of electromagnetic waves from particles and objects and modeling of optoelectronic systems. We will only illustrate the method with respect to planar electromagnetic wave propagation problems at normal incidence. However, prior to this we shall give an overview of PDEs, including how they are classi ed into elliptic, parabolic, and hyperbolic types.

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