Methods and systems to control an adaptive time-step

A system, comprising:

• an input device configured to receive a set of nonlinear differential algebraic equations that describes the system, and a set of control parameters;
• a computing resource;
• and
• a storage device coupled to the computing resource, wherein the storage device is configured to store a plurality of software instructions, wherein when executed, the software instructions cause the computing resource to:
• calculate a set of solutions to the set of nonlinear algebraic equations by using a value for a first time step, wherein each of the solutions corresponds to a node of the system and a time step is an interval between a previous time point and a current time point;
• determine whether a maximum value of local truncation error associated with a first solution of the set of solutions is greater than a threshold;
• and
• based on the maximum value of the local truncation error being greater than the threshold, iteratively calculate a coupled set of equations to generate a second time step so as to make a maximum value of local truncation error associated with a set of solutions to the coupled set of equations not greater than the threshold, wherein the coupled set of equations comprises the received set of nonlinear algebraic equations and a local truncation error equation corresponding to the first solution, with a time step that is an unknown variable in the coupled set of equations.

A non-transitory, computer-readable storage device containing instructions that, when executed by a computing resource, cause the computing resource to:

• calculate a set of solutions to the set of nonlinear algebraic equations by using a value for a first time step, wherein each of the solutions corresponds to a node of the system and a time step is an interval between a previous time point and the current time point;
• determine whether maximum value of local truncation error associated with a first solution of the set of solutions is greater than a threshold;
• and
• based on the maximum value of the local truncation error being greater than the threshold, iteratively calculate a coupled set of equations to generate a second time step so as to make a maximum value of local truncation error associated with a set of solutions to the coupled set of equations not greater than the threshold, wherein the coupled set of equations comprises the received set of nonlinear algebraic equations and a local truncation error equation corresponding to the first solution, with a time step that is an unknown variable in the coupled set of equations.