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Differential Equ
ation in matlabThe MathWorks - Support - Differential Equations in MATLAB

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1510 - Differential Equations in MATLAB
Differential Problems in MATLAB 1. What Equations Can MATLAB Handle? 2. Where Can I Find Tutorials or Additional Information? Frequently Asked Questions 3. What Changes in Syntax Exist for ODE Solvers? 4. How Do I Reduce the Order of an ODE? 5. How Do I Solve Time-Dependent ODEs? 6. How Do I Use a Fixed Time Step? 7. How Do I Use Stochastic Differential Equations? Examples 8. Systems of Equations 9. Boundary Value Problem (BVP): Channel Flow Stiffness 10. What Is Stiffness? 11. Implicit vs. Explicit Methods 12. Examples Options 13. How Can I Change Options When Solving a Differential Equation? 14. What Option Parameters Can Be Modified? 15. How Can Options Be Used as Functions? Differential-Algebraic Equations and their Index 16. How Can Differential Algebraic Equations Systems Be Solved in MATLAB?

Section 1: What Equations Can MATLAB Handle?
MATLAB provides functions for solving several classes of problems involving differential equations: 1. Initial Value Problems for Ordinary Differential Equations (ODEs) This is the most popular type of problems solved using MATLAB ODE solvers. Initial value problems are typically solved with ODE45 for the nonstiff case, and with ODE15S in the stiff case. (For an explanation of Stiffness, refer to the section "What is Stiffness".) 2. Initial Value Problems for Differential Algebraic Equations (DAEs) These are frequently encountered in areas where conservation laws dictate a constant relationship between some variables. MATLAB can solve DAE's of index 1 using ODE15S or ODE23T. (For an explanation of index, refer to the section DAEs
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