![]() ![]() This is only computed if the method is an auto-switching algorithm. maxeig: Maximum eigenvalue over the solution.ncondition: Number of calls to the condition function for callbacks.nnonlinconvfail: Number of nonlinear solver convergence failures.nnonliniter: Total number of iterations for the nonlinear solvers.njacs: Number of Jacobians calculated during the integration.nsolve: The number of linear solves W� required for the integration.nw: The number of W=I-gamma*J (or W=I/gamma-J) matrices constructed during the solving process.nf2: If the differential equation is a split function, such as a SplitFunction for implicit-explicit (IMEX) integration, then nf2 is the number of function evaluations for the second function, i.e.If the differential equation is a split function, such as a SplitFunction for implicit-explicit (IMEX) integration, then nf is the number of function evaluations for the first function (the implicit function) Statistics from the differential equation solver about the solution process. Differential Equation Solver Statistics (destats) DiffEqBase.DEStats - Type The iterator interface simply iterates the value of tslocation, and the animate function iterates the solution calling solve at each step. What this means is that for ODEs, the plots will default to the full plot and PDEs will default to plotting the surface at the final timepoint. tslocation=i means that the plot recipe will plot the ith timepoint. tslocation=0 for spatial problems (PDEs) means the plot recipe will plot the final timepoint.tslocation=i means that it will only plot the timepoint i. tslocation=0 for non-spatial problems (ODEs) means that the plot recipe will plot the full solution.Its values have different meanings between partial and ordinary differential equations: Lastly, there is a mutable state tslocation which controls the plot recipe behavior. Further, the field destats contains the internal statistics for the solution process, such as the number of linear solves and convergence failures. Additionally, the field dense is a boolean which states whether the interpolation functionality is available. The problem object prob and the algorithm used to solve the problem alg are included in the solution. The solution interface also includes some special fields. Note that the solution object acts as a vector in time, and so its length is the number of saved timepoints. One can comprehend over the values using: For example, say the solution type holds du, the derivative at each timestep. One can use the extra components of the solution object as well as using zip. Using the tuples(sol) function, we can get a tuple for the output at each timestep. The solver interface also gives tools for using comprehensions over the solution. This allows one to use pre-allocated vectors for the output to improve the speed even more. Instead of working on the Vector idxs = nothing, continuity = :left) t which holds the times of each timestep.ĭifferent solution types may add extra information as necessary, such as the derivative at each timestep du or the spatial discretization x, y, etc.u which holds the Vector of values at each timestep.Internally, the solution type has two important fields: For example, it has an array interface for accessing the values. The solution type has a lot of built-in functionality to help analysis. Edit on GitHub Solution Handling Accessing the Values Reduced Compile Time, Optimizing Runtime, and Low Dependency Usage.Specifying (Non)Linear Solvers and Preconditioners.Dynamical, Hamiltonian, and 2nd Order ODE Solvers.Non-autonomous Linear ODE / Lie Group ODE Solvers.Dynamical, Hamiltonian and 2nd Order ODE Problems.Non-autonomous Linear ODE / Lie Group Problems.Differential Equation Solver Statistics (destats).Interpolations and Calculating Derivatives.Common Solver Options (Solve Keyword Arguments).Solving the heat equation with diffusion-implicit time-stepping. ![]() ![]() ![]() An Implicit/Explicit CUDA-Accelerated Solver for the 2D Beeler-Reuter Model.Finding Maxima and Minima of ODEs Solutions.Code Optimization for Differential Equations.Getting Started with Differential Equations in Julia.DifferentialEquations.jl: Efficient Differential Equation Solving in Julia. ![]()
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