Initial Value Problems
Even from casual observation it is apparent that most physical phenomena vary both in space and time. For example, the temperature of the atmosphere changes continuously at any given location and it varies significantly from point to point over the surface of the Earth. A consequence of this is that mathematical models of the real world almost inevitably involve both time and space derivatives. The objective of this book is to examine how to solve such problems using a computer; but to begin, we first consider more simplified situations. In this chapter we study problems involving only time derivatives and then in the next chapter we examine spatial problems. The remaining chapters then examine what happens when both time and space derivatives are present together in the problem.
KeywordsTruncation Error Euler Method Logistic Equation Initial Value Problem Trapezoidal Method
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