I'm using the package deSolve in R to model a biological ODE system, however I have the problem of, with certain parameters or with certain initial conditions, the ode solver produces negative values, which make no sense in a biological scenario.
Is there a way to avoid this without recurring to logarithms?
Hi, I agree with Marc's remarks. A possibility would be also to test MATLAB for solving the same equation.
Reading about the problem my recommendation would be to try to find out why the system produces the negative values. If you want to model the biological system, then there might be something fundamentally wrong in the modelling if it allows it to become negative; so there might be little point in simulating something that is not representative of the physics you want to use. If you find out what is wrong, then perhaps you can fix and then the problem goes away.
Dear Afonso Dimas Martins
If you solve a homogeneous quadratic ordinary differential equation, you will encounter three modes. 1. The Characteristic Equation Having Real Distinct Roots 2- The Characteristic Equation Having Repeated Roots 3. The Characteristic Equation Having Complex Roots Therefore, the equation will be solved by one of the above methods.
try to solve with MATLAB ode45 first and use the ''persistent' keyword to obtain all output including any exitflags to see if you have warnings. the i suggest you switch to ode23s or ode15s for stiff differential equations. Or as might be the case, you might have the model wrong, maybe a typo or a parameter off by an order of magnitude
Don't know deSolve but can you add constraints to your problem? Try the FortranCalculus (FC) language that got its start by NASA's Apollo Space program. FC solves constrained ODEs with little effort, its easy to learn.
FC-Compiler™ application is a (free) Calculus-level Compiler that simplifies Tweaking parameters in ones math model. FC solves Algebraic through Ordinary Differential Equations Equations; Laplace transforms; etc. FC is based on Automatic Differentiation that simplifies computer code to an absolute minimum; i.e., a mathematical model, constraints, and the objective (function) definition.
Most math Modeling, Simulations, & Optimizations can be easily solved with a Calculus-level language/compiler. A half-hour per problem should be enough time to code and execute most math problems. Solves Algebraic Equations through Ordinary Differential Equations, for more visit http://fortrancalculus.info/apps/fc-compiler.html . Equations may be implicit, non-linear, Boundary Value Problems (BVP), Initial Value Problems (IVP), etc. Download, install, & execute some demo problems. Simple and its Freeware! (PDE solvers are in the works!)
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