The rapid and impressive results obtained through the application of numerical methods of analysis to electrodynamics created the rather false impression (es- cially to inexperienced engineers) that all problems were solved long ago or that some of them were not solved because one lacked suf?cient time. However, it is suf?cient to formulate these problems clearly, to give the task to a programmer to create the corresponding program, and to let a computer “think. ” It is only left for an engineer to make the corresponding plots and to explain calculation results if the latter do not agree with existing physical notions. However, de?nite conf- mity to natural laws starts inevitably to appear while realizing this sequence of steps: the problem is prepared for calculations more thoroughly—the probability to obtain the correct answer is higher, and the obtained information is richer and more interesting—the calculated algorithm is simpler; and as expenditure of calculation time is less, correspondingly, the problems to solve effectively are more complex. Theproblemformulationisnotonlycompilationofinitialequationsandanumerical algorithm. It is necessary to foresee a qualitative character of the obtained results and expected order of values, to reveal the peculiarities of the searched solution, complicating its numerical realization and, as a result, choosing the known solution algorithm or working out a new one. If this work has not been done properly, then unexpected anomalies may appear during the numerical calculation process, and the results can be the basis for the most sensational “discoveries.

The rapid and impressive results obtained through the application of numerical methods of analysis to electrodynamics created the rather false impression (es- cially to inexperienced engineers) that all problems were solved long ago or that some of them were not solved because one lacked suf?cient time. However, it is suf?cient to formulate these problems clearly, to give the task to a programmer to create the corresponding program, and to let a computer “think. ” It is only left for an engineer to make the corresponding plots and to explain calculation results if the latter do not agree with existing physical notions. However, de?nite conf- mity to natural laws starts inevitably to appear while realizing this sequence of steps: the problem is prepared for calculations more thoroughly—the probability to obtain the correct answer is higher, and the obtained information is richer and more interesting—the calculated algorithm is simpler; and as expenditure of calculation time is less, correspondingly, the problems to solve effectively are more complex. Theproblemformulationisnotonlycompilationofinitialequationsandanumerical algorithm. It is necessary to foresee a qualitative character of the obtained results and expected order of values, to reveal the peculiarities of the searched solution, complicating its numerical realization and, as a result, choosing the known solution algorithm or working out a new one. If this work has not been done properly, then unexpected anomalies may appear during the numerical calculation process, and the results can be the basis for the most sensational “discoveries.

The rapid and impressive results obtained through the application of numerical methods of analysis to electrodynamics created the rather false impression (es- cially to inexperienced engineers) that all problems were solved long ago or that some of them were not solved because one lacked suf?cient time. However, it is suf?cient to formulate these problems clearly, to give the task to a programmer to create the corresponding program, and to let a computer “think. ” It is only left for an engineer to make the corresponding plots and to explain calculation results if the latter do not agree with existing physical notions. However, de?nite conf- mity to natural laws starts inevitably to appear while realizing this sequence of steps: the problem is prepared for calculations more thoroughly—the probability to obtain the correct answer is higher, and the obtained information is richer and more interesting—the calculated algorithm is simpler; and as expenditure of calculation time is less, correspondingly, the problems to solve effectively are more complex. Theproblemformulationisnotonlycompilationofinitialequationsandanumerical algorithm. It is necessary to foresee a qualitative character of the obtained results and expected order of values, to reveal the peculiarities of the searched solution, complicating its numerical realization and, as a result, choosing the known solution algorithm or working out a new one. If this work has not been done properly, then unexpected anomalies may appear during the numerical calculation process, and the results can be the basis for the most sensational “discoveries.