International audienceThis paper describes mathematical and software developments for a suite of programs for solving ordinary diierential equations in Matlab

This book is for people who need to solve ordinary differential equations (ODEs), both initial value problems (IVPs) and boundary value problems (BVPs) as well as delay differential equations (DDEs). These topics are usually taught in separate courses of length one semester each, but Solving ODEs with MATLAB provides a sound treatment of all three in about 250 pages. The chapters on each of these topics begin with a discussion of "the facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed-but only the methods most widely used. Although the treatment of each method is brief and technical issues are minimized, the issues important in practice and for understanding the codes are discussed. Often solving a real problem is much more than just learning how to call a code. The last part of each chapter is a tutorial that shows how to solve problems by means of small but realistic examples.

Our goal was to make it as easy as possible to solve a large class of boundary value problems (BVPs) for ordinary differential equations in the Matlab problem solving environment (PSE). We present here theoretical and software developments resulting in bvp4c, a capable BVP solver that is exceptionally easy to use.

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