![]() ![]() The numerical simulations reveal that our proposed iterative method clearly shows better performance, where the computational cost of the involved nonlinear function is higher than the computational cost for solving five lower and upper triangular systems. The distinctive feature of the underlying multi-step iterative method is the single call to the computationally expensive nonlinear function and thus offers an increment of additive-factor of five in the convergence order per single call. ![]() The computed LU factors are used in the multi-step part for solving five systems of linear equations that make the method computational efficient. ![]() The direct inversion of Jacobian is avoided by computing LU factors. Im trying to recreate graphs from a modeling paper by plotting a system of differential equations in MatLab. For a single instance of the iterative method we only compute two Jacobian and inversion of one Jacobian is required. The general formula of convergence order is 5 ( m − 2 ) where m ( ≥ 3 ) is the step number. Finding a solution to a differential equation may not be so important if that solution never appears in the physical model represented by the system, or is. In the following example, a function x (t) is a solution of the nonlinear differential equation (x' + 2x)2 3 subject to the initial conditions x (0) 0. matlab will list all solutions regardless. The convergence order of the base method is five, and each step of multi-step part adds additive-factor of five in the convergence order of the base method. Solve systems of nonlinear equations in serial or parallel Find a solution to a multivariable nonlinear equation F ( x) 0. It is important to note that even if there are initial conditions, nonlinear differential equations can have more than one solution. These other solvers are good tools to keep in mind if your solution is hanging sometimes one of the others will work and it will either give you what you want, or indicate that you have another problem somewhere else. The proposed method is divided into a base method and multi-step part. Basically I solved it with ode15s and ode23s and found that the solution was unstable (population went off to infinity). Construction of multi-step iterative method for solving system of nonlinear equations is considered, when the nonlinearity is expensive. ![]()
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